Here, I want to generalize that discussion. Under what conditions does public spending on higher ed increase the number of people in college, and under what conditions does it just enrich Kaplan and the Harvard endowment? More broadly, it seems to me that the price effect of subsidies is a neglected argument for direct provision of public goods.
Formally, a subsidy is just a negative tax, and like a tax, its incidence depends on the relative elasticities of supply and demand.  If supply is less elastic than demand, most of the cost (of a tax) or benefit (of a subsidy) will fall on the producer; if demand is
This argument got brought out during the 2008 presidential campaign to explain why proposals to deal with high gas prices by cutting the gax tax were foolish: With the short-term supply of gas highly inelastic, almost the whole tax fell on producers. As long as refineries were running at full capacity, changes in the gas tax would not affect the price at the pump.
So far, so familiar. The interesting question is what happens when we generalize this logic to other areas, like higher education. Imagine a state that's considering a choice between spending, let's say, $1 million either subsidizing its public university system, enabling it to keep tuition down, or as grants to college students to help them pay tuition. On the face of it, you might think there's no first-order difference in the effect on access to higher ed -- students will spend $1 million less on tuition either way. The choice then comes down to the grants giving students more choice, fostering competition among schools, and being more easily targeted to lower-income households; versus whatever nebulous value one places on the idea of public institutions as such. Not surprisingly, the grant approach tends to win out, with an increasing share of public support for higher education going to students rather than institutions.
But what happens when you bring price effects in? Suppose that higher education is supplied inelastically, or in other words that there are rents that go to incumbent institutions. Then some fraction of the grant goes to raise tuition for existing college spots, rather than to increase the total number of spots. (Note that this must be true to at least some extent, since it's precisely the increased tuition that induces colleges to increase capacity.) In the extreme case -- which may be nearly reached at the elite end -- where enrollment is fixed, the entire net subsidy ends up as increased tuition; whatever benefit those getting the grants get, is at the expense of other students who didn't get them.
Conversely, when public funds are used to reduce tuition at a public university, they don't just lower costs for students at that particular university. They also lower costs at unsubsidized universities by forcing them to hold down tuition to compete. So while each dollar spent on grants to students reduces final tuition costs less than one for one, each dollar spent on subsidies to public institutions reduces tuition costs by more. 
The same logic applies to public subsidies for any good or service where producers enjoy significant monopoly power: Direct provision of public goods has market forces on its side, while subsidies for private purchases work against the market. Call it progressive supply-side policy. Call it the general case for public options. The fundamental point is that, in the presence of inelastic supply curves, demand-side subsidies face a headwind of adverse price effects, while direct public provision gets a tail wind of favorable price effects. And these effects can be quite large.
This is exactly the argument of the Austan Goolsbee paper cited in the post below. As he shows, capital goods (and the scientists and engineers responsible for them) are in very inelastic supply, especially at time horizons of a few years or less. So almost the entirety of subsidies to research and development is collected as rents by the suppliers of these goods; actual R&D activity increases by little or nothing. Of course Goolsbee, like most economists who've studied this, only considers the negative side, the case against subsidies. But the exact logic that leads him to conclude that the impact of subsidies for R&D buyers is dampened by price effects, should lead him to conclude to that the impact of direct public provision (e.g. training scientists and engineers) would be multiplied by them.
It's easy to think of similar cases -- housing would be another obvious one, or the original public option, health insurance. But let's consider an example of the same logic in reverse: wage subsidies like the EITC. Here, we want to subsidize the "producer" (the worker) while it's the "consumer" (the employer) who may have the market power to claim the subsidy as a rent. What's nice about this example is that we have a good study by Jesse Rothstein that estimates the size of the price effect. 
Rothstein starts by observing that most estimates of the EITC's impact assume an infinitely elastic demand for labor, or in other words, a fixed wage. (This is equivalent to the assumption of elastic supply in the cases above.) As he shows, once we allow for realistically inelastic labor demand, a very large fraction of EITC payments is captured by employers rather than received by workers. Even worse, ineligible workers also see a reduction in wages, since they are competing with the EITC-subsidized ones.
When I allow for a finite demand elasticity, ... I find that the EITC produces sizable reductions in equilibrium wages that offset many of its benefits to low-skill workers. With my preferred parameters, the net-of-tax incomes of women with children rise by only $1.07 for each dollar spent on the program. Moreover, this is accompanied by a decline of $0.34 in the net-of-tax incomes of women without children... The contrast with the [Negative Income Tax] is dramatic. The NIT imposes positive tax rates on earnings, leading to net reductions in labor supply among eligible women and thereby to increased wages. A dollar of government expenditure on the NIT produces a $0.97 increase in the after-tax incomes of women with children and an increase of $0.42 for women without children.In other words, the same dollar spent on a negative income tax (or public employment program, tho Rothstein doesn't discuss it) results in twice as large an increase in the wages of low-income workers as a dollar spent on the EITC. And even the gains that do come from the EITC depend on increasing the hours worked by the recipients, which is a cost; those hours would otherwise not be wasted but used for "consumption of leisure" (Rothstein's unfortunate economism) or, more realistically given that the main recipients of the EITC are single mothers, for child care. Taking the additional working hours into account,
a dollar of EITC spending produces net increases in the welfare of women with children with cash value of only $0.83... Employers of low-skill labor capture $0.36 via reduced wage bills, while the welfare of (EITC-ineligible) childless women falls by the equivalent of $0.18. Moreover, this obscures the even worse welfare consequences for single mothers, the primary group targeted by the EITC. Fully 55% of the marginal EITC dollar given to this group is captured by employers through reduced wages, and single childless women lose almost exactly as much as single mothers gain. Again, the NIT offers a dramatic contrast: The welfare of women with children rises by the equivalent of $1.32 and that of women without children by $0.23, with transfers of $0.55 from employers to their workers magnifying the direct transfer from the government.So in this fuller analysis, a dollar paid directly to low-income households goes three times as far as a dollar of wage subsidy. And the market power of employers, while often substantial, is almost certainly lower than that of suppliers of goods like higher education or urban housing. So in those cases we should expect price effects to be even larger.
This argument seems straightforward and logical, and has some empirical backing. But it's only very rarely made in support of direct provision of public goods. One can speculate why that might be. But the important thing is those of us seeking an incremental de-marketization of society, should recognize that the logic of the market is often on our side.
 For the hypothetical non-economist reading this, elasticity means how much one number changes in response to a change in another. When we say elasticity of supply or elasticity of demand, we implicitly mean elasticity with respect to price. So for instance, a demand elasticity of 0.5 means that if the price rises by 10%, demand will fall by 5%.
 The case is slightly complicated by the fact that higher education is not only rationed by price. So a subsidy to students has the additional effect of making colleges more selective by academic criteria, while a subsidy to institutions makes them less so. One could argue either side as far as which of these effects is desirable, but either way they don't change the basic picture in terms of cost and access.
 Thanks to my friend Suresh for pointing me to this paper. He also suggests that "there is a general Polanyi-esque point here about how land, labor, and capital have 'supply' curves that don't respond generally to short-term prices terribly well."