Not that state schools are much cheaper these days, but do you really think it's good advice to suggest accumulating 200K+ in debt to get an undergrad degree?
So yes, I strongly advice any high school student from any economic background to apply.
Edit: changed "keeled" to "need" in first sentence; damn phone auto-complete!
I went with the liberal arts school, and haven't been disappointed. I'll have debt, but I've have a job lined up to pay it off.
MIT makes it clear that they want you there regardless of whether you can pay. I definitely recommend that any high school student who's interested and passionate about technology apply, and not weigh the cost too heavily in considering where to go.
It really doesn't hurt to apply - I got my aid package before I had to decided to commit to any school.