He could have simply said, "No".
Good point. It's quite understandable the President didn't answer "yes" and call Islam what it is (a cult of death) when asked by that interviewer if it were true that he wants to destroy both it and its adherents. Doing so would've been insane, obviously. But at the same time he didn't need to go to the other (and in this case false and ridiculous) extreme and say that Islam preaches peace and that all religions pray to the same Deity.
As you said, he could've simply said "no." ...and then added that the actions of the U.S. over the past few years, releasing tens of millions of Islamics from tyranny and oppression, proves it.