I guess the idea is that a much larger number of people could make use of math or science if they weren't predisposed to think that they belong in an incapable segment?

Yes. And more people would go into math and science.

My suspicions are somewhat based on the article from a couple of years back, which claimed that many freshman computer science students seem to simple lack the basic mental model building ability needed to start comprehending programming.

That's a very interesting article. I think that the level of, and type of abstraction necessary to program is already orders of magnitude beyond where most people stop being willing to do math. My own experience in regards to tutoring students who aren't doing well in math is that one of the primary issues is one of confidence: students of all types think they aren't good at math and thus freeze up when they see something that is slightly different from what they've done before. If they understand that they aren't bad at math or that they don't need to be bad at math, they are much more likely to be willing to try to play around with a problem a bit rather than just panic.

I was an undergraduate at Yale which is generally considered to be a decent school that admits people who are by and large not dumb. And one thing that struck me was that even in that sort of setting, many people minimized the amount of math and science they took. When asked about it the most common claim was that they weren't good at it. Some of those people are going to end up as future senators and congressman and have close to zero idea of how science works or how statistics work other than at the level they got from high school. If we're lucky, they know the difference between a median and a mean.