With all due respect, dgroundhog, I regard it as highly plausible that Mr. Gheit was either extrapolating, inferring, or otherwise just plain assuming that Obama has identified himself as a Muslim. Or, Mr. Gheit was simply being sloppy and careless in relating the contents of his conversation.
At the same time, it is likewise quite plausible that Obama did everything he could - without making an explicit statement - to foster Gheit's inclination to believe and to make a tacit assumption. Obama is, after all, a politician, and is sure to understand how to use weasel words, vague references, and innuendo - wink, wink... nod, nod - to lead his listener down the garden path without sticking his neck out and making a definite statement.
Obama is not so stupid as to needlessly claim, in a quotable fashion, to be a Muslim.
Regards,
Similarly, you could say it is ‘plausible’ that Obama told him he would nuke the world.
You could say a lot of things that aren’t in the article, but in the end we are left with what the article actually tells us - and it says Obama told him he was a muslim.