I’m not sure where you got this idea. I don’t know about every department, but as a whole, Brown is very well known and respected. People definitely know it’s Ivy League. And, at least in some departments, there is significant collaboration with Harvard and Yale, as wells as the other Ivies.
I have heard from 3 out of the 4 schools I applied to, and am thinking about just making a decision now. I have no idea when I'll hear from the 4th place and may give up on it, so that I can make a decision.
In my experience, something to think about is that programs care as much about where you are going (in terms of your interests and research), as they care about where you've been academically. That is, they want you to have the background, languages etc for your stated goal to seem logical and achievable. But, they seem to also especially care about whether your academic goals fit with their program, professors, field, etc.
Does anybody know if Princeton does interviews for (all) potential candidates for Religious Studies? If I haven't gotten one, does that mean I'm out? It doesn't look as if anyone has heard from them yet...