I also do a fair bit of interviewing at Fog Creek and we don't really care about which school you went to. We look for smart people who get things done. It's as simple as that.
That doesn't really jive with the not caring "about which school you went to" bit. If that's the criteria it eliminates all but 2 of the top 25 public universities which is flat out ridiculous.
In an interview the school you go to doesn't really matter if you can't code.
A great github account would probably help you more in our interview process than a degree from MIT.
That doesn't mean you have to go to one of those schools to get in - which school you went to is treated as a weak signal in the resume reviews, and is ignored for the rest of the process. I went to a public school that falls outside of the 30% rule, for example, and another from my school will be joining us this summer.
If you are on a student visa (which clearly a full time employ isn't), then there are some hoops to jump through in order to work, but I am not familiar with the necessary steps.