This is true. ISIL is very much shaped by Islam, a very reactionary form that goes back to something most others diverged from in the middle ages. But like I said here, I think Obama is in a very poor position to acknowledge that, since the nuance of his remarks is likely to be stripped and any subtext can hurt people.
This explains it well enough to me; the main concern is to be sure not to have people think the west and Islam are enemies. Because that’s a message people are looking for. It’s what Trump has been selling, it’s the whole reason his people care that Islamic terrorism is singled out in the first place. I’m not sure how people think saying he’s right is supposed to help counter him, but I am sure it’s a message that gets people hurt.
Obama is describing religion as he would like it instead of as it is, but for his position I think he is saying the right thing. If not in terms of politics against Trump, in terms of actually discouraging marginalization or radicalization of religious groups.