I'm a sophomore at Tisch now. The last time I ever thought about the copyright on my student films was when I was applying to film schools and Chapman made a big deal out of it. Since then it hasn't mattered at all. Don't worry about it. It's completely moot.
Student films never go anywhere. There's honestly no reason for you to hold even intellectual rights on them. Trust me, virtually nothing you make in film school will be commercially useful. This is for two reasons: 1) 99.9% of filmmakers aren't NEARLY as talented as they think they are, and 2) the resources given to you are not great enough and the assignments are too unique so there's usually no reason your creation would be of interest to non-filmmakers anyway.
That said, there certainly are *some* students at NYU who have their final thesis films broadcast (documentaries, mainly) but that's post-graduation and long after the film's educational purpose has run out. Any of these schools would be more than happy to not only let you broadcast, but help you get there.
We've already spent so much time discussion copyrights it's ridiculous. It's the LAST thing that should be on your mind right now.
As for NYU vs. USC vs. Chapman, I'd rank and attend them in that order. I faced the same decision you are facing now and picked NYU for two reasons: I did NOT want to live in LA and after touring the schools decided that, even besides location, NYU offered the best environment for me to grow as an artist. I was not impressed with Chapman academically or intellectually (though they have great facilities and bla bla that stuff doesn't really matter trust me). I was not impressed with USC on an emotional/personal level (everyone there was really rude and stuck-up to me for some reason) but WAS impressed with NYU on every level.