In all honesty Rob I agree with you. They do have the right to buy the property, turn it into a community center and even pray in it. But is it "wise"? Of course one could ponder, "is it wise to build a gay bar next to a Muslim community center/mosque"? Probably not. It might offend somebody.
If you note from 0:18 - 0:32 even President Obama states that they have the right but the wisdom of their decision still up in the air...at least for him.