False. Obama held several "private sessions", often inviting only left-leaning journalists [0]. I think people are conflating "press gaggle" with official press briefings.
"According to a source who saw the group leaving the Roosevelt Room, where the meeting was held, those present included John Harwood of CNBC and The New York Times, Juan Williams of The Hill and Fox News, and Washington Post columnists Eugene Robinson and Jonathan Capehart."