Well, I can tell you that not only did I not graduate from an elite school, I didn't even graduate from college. I've never had a problem finding work at startups. Very rarely does anyone care -- it's always about whether or not you have the necessary skills.
Maybe not intentionally, but if your workforce is mostly MIT/Stanford grads and part of your recruiting strategy involves sending employees to their Alma Maters and leveraging their social networks, there is a bit of positive feedback in play biasing recruitment towards MIT/Stanford. Totally anecdotal, but there was no Apple recruitment presence at the school I went to until a few students were hired into Apple.
I've done 100+ interviews and never once did the school come in as a prerequisite.
The teams are generally small. We make the coding exercises intense. You will be asked to code onsite. At the end of the day, we just want a guy that we're not constantly cleaning up after.
A few companies I know only do college recruiting from specific schools (the elite schools). The Director of College Recruiting for one of those companies told me - we only go to those schools for recruiting events; however, anybody from any school in the US can apply for any vacancy listed on our website; the person will simply have a longer/larger pipeline to go through.
I should add that the companies that I'm referring to are NOT startups.