1) I often see woodchucks walking along the breakdown lane of the highway, but very rarely do I see them run over. I bet there's something interesting going on there.
2) I put a terrarium in my freezer, and after a year a worm in the bottom was still alive. I bet there's something interesting going on there.
And so on.
It might be the case that entrepreneurship is a "weak patterned" field, i.e. that there are only patterns in bad ideas. For example:
1) No one wants to use my product.
2) My product costs more money than it makes.
3) There is no way of implementing my product.
4) It's like MySpace but for knitter's in Canada! (Going from general demographic to niche demographic)
5) It's like MySpace but with this cool new feature! (It's a feature, not a product)
6) It's like Google, but with a tag cloud! (Doesn't give a better answer to the user's questions)
And so on. Just looking through other people's bad ideas I think we can easily find 20 or 30 common patterns.
So even if it's not possible to teach what a good idea is, it certainly is possible to teach "the funnel method" of eliminating bad ideas.
And while there may be no patterns in good ideas, I think that, as you suggested, there are some very clear patterns in where good ideas come from.
Incidentally, I have this theory that most good business ideas start with "I have this theory..."
Plus it's probably just not that teachable. I think the most you can do is teach people where to look for good ideas: where to find cracks in conventional wisdom, what types of questions tend to produce fruitful answers, and so on.
BTW, YC doesn't care how much time people have spent in classrooms. The reason we like graduates is simply that they can't retreat to school if things get tough.