Although I take his point and never promote "positive rights" thinking here, I think there are a lot of problems with this sort of logic. First and foremost, if you are the sort of person that thinks people are entitled to these sorts of things - for whatever reason - you're not failing to learn from experience if you critique a public system that fails. Let's say you think these things should be provided by the market instead. If the market leaves a lot of people unprovided for, and frustrates the people it does provide for with red tape, is that "empirical evidence" against your anti-positive rights prespective? Of course not. You console yourself with arguments that the market will correct itself as people react to these failures. That's really all the commencement speaker is doing here. He doesn't seem to me to be failing to integrate his experiences - he seems to be considering his experiences deeply and responding to them. People aren't bound to develop their understanding of rights from empirical experience with the efficacy of certian systems.
The other thing that bothers me about this sort of logic is that it presumes that whenever a government does something, people always generalize that to public provision in general. This is really an odd way of looking at things. When a particular firm fails to satisfy you, it's not sensible to say "well I guess the market can't provide X". Instead, you seek out firms that do the job better and console yourself with arguments that the price mechanism will privelege those firms. That seems to me to be all people are doing when they see a failure of government but still want to seek out a better public solution. It would be awfully myopic to take one failed approach to public provision and rule out that option. Kate and I are dealing with really obnoxious extra charges that our phone company adds no matter how many times we call them and remedy the problem. If it gets bad enough, I may consider switching phone companies - but I'm not going to start demanding state-run phone companies! Similarly, when the government fails at something that I consider to be a valid public service, my first reaction is going to be to try to change how the government works, not abandon my understanding of the appropriate role of government.
There are a few other things I don't think people consider enough in these sorts of discussions:
1. There's a difference between "positive rights" and "legal rights". It may be reasonable to say that "everyone has a right to a good education" and understand that that right will go unsatisfied sometimes, without arguing that the government ought to provide that education. Anarchists, after all, generally acknowledge some set of "rights" without expecting any government provision.
2. Assessing the value of public services needs to be done with (1.) marginalism and (2.) general equilibrium effects in mind. I cannot stress this enough. It's meaningless, for example, to show that private school children do better than public school children. Of course they do. If they didn't do considerably better they wouldn't shell out tuition for it. Even more cost effective private schooling shouldn't compare averages with public schools. The appropriate comparison isn't between an existing public school and an existing private school. It's between a system of public schools (presumably with some private) and a system without public schools. Too many people who talk about this subject take a marginal effect on the intensive margin (putting a given similarly placed student into private or public school) and use it to try to say something about the extensive margin (comparing a system of public or no public schools). These are entirely different research questions. You can have too much public school on the intensive margin but still have the right approach (public provision) on the extensive margin. These intensive/extensive margin differences matter tremendously - they lead people to say dumb things like "recessions are caused by high wages".
3. Public and private, and government and market are not mutually exclusive. You can have market-based public intervention (i.e. - charter schools, carbon taxes). You can have the coexistence of public and private provision (NASA and SpaceX). Advocates of certain public solutions should not be confused with opponents of private solutions.