Actually, you can get to NASA from a lot of places. Just running some linkedin for nasa and aerospace engineer, I see Florida Tech, Saint Louis U, Missouri Science & Tech, San Jose State, Towson, Rowan. Those are just the first 6 or 7 I picked up. Some had grad degrees to.
I think you can get to NASA from anywhere. UAH is a great school - but I don’t think NASA is that concentrated.