Yes, but do you really think that he says what he truly thinks when he's making a speech to the nation? He's trying to get people to agree with him, not have an intellectual debate. My objection is that if you're going to talk about how "intellectuals" view the classics, you should be talking about scholars. I don't think it's fair to lump all intellectuals in with some speech Obama made.
Well, I'll cede the point although I think it's just a case of Obama "appealing to the expert" with regard to political science. That and similar is a valid example of the classics pervading our culture. Anyway, scholars themselves still revere Plato and Aristotle to a huge extent. I think it's a reasonably fair generalization.
To add some anecdotal evidence, I'm taking five courses this semester at uni and within the first three weeks each of my professors had referenced both Plato and Aristotle. The philosophy course and polisci course excused, for the nonfiction writing course, the late 20th century literature course, and the intro to film course, it felt a tiny bit out of place.