A couple of thoughts:
1. This program may have cut-off scores, and if you don't meet those, you're not getting an interview regardless of how good you are on the rotation. This happens all the time: I've known of people who were awesome on rotations but have been told straight up by PDs at their home programs that by the numbers they will not match, period, at their home institution. If that's the case for this program, you're wasting your time.
2. Everyone is constantly talking about burning bridges and fellowship and what-not. When I think of burning bridges, I think of "cussing everyone out and telling them where to go", not "canceling an away because it doesn't make sense to do it if you're not going to get in". Do you really think egos are so fragile that they're going to hold a 3+ year grudge against you for not doing an away rotation when it doesn't make sense? Heck, they probably have a wait list of people wanting to do a rotation there. And if their egos ARE that fragile, is that really somewhere you'd want to work/be a fellow at anyways?
My advice...talk to your adviser, possibly your home program PD, and ask what they think you should do. I'd be inclined to e-mail the PD of that program and explain the situation, and see if there's a chance. If there's no chance to get an interview, why waste your time/money? And if they can't understand that, then they're not the kind of people you'd wanted to be associated with, ever.