Huh? The "truth" is that according to our constitution, according to what is "right" and according to the principles of freedom, liberty and religious tolerance, we shouldn't ban people from building religious structures on private property as long as it doesn't violate local ordinances or zoning requirements.
Besides that you seem to be terribly confused. Obama made a statement based on the principle that people can build any brand of religious institution on private property. The ability for this mosque to be built did not hinge on his approval. His comments were certainly related to the issue created by this particular mosque, but not related to his feelings about the building of this particular mosque. Again, Obama has no role in deciding if this mosque is built or not. He did not make a "decision" to allow it to be built. You understand that, right?
This may hurt his standing among simpletons and religious bigots. If that is what makes up the majority of voters then we have much worse problems than a moasque being built several blocks from the site of one of our nations greatest tragedies.