When the national media (NY Times, Washington Post, Chicago Tribune) reported that Obama was Hawaii-born the year prior, clearly the source for that was Obama.
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Then similarly, “when the national media reported that Obama” (AP, LA Times, iirc) left for Indonesia when he was two years old, then by the same token “clearly the source for that was Obama.”
Perhaps. Though on that point Obama DID leave for Indonesia after his parents divorced and his mother remarried. Age 8 versus age 2 is a bit of a minor quibble. It seems more likely here the reporter mixed notes about the dates of Dunham's separation/divorce from BHO Sr and remarriage to Soetoro. A lot was going on in those years.
By contrast, it is an error of much greater magnitude for "born in Kenya" to end up being reported as "born in Hawaii," especially given the former stood to make the story all the more compelling.
In any event, the "born in Hawaii" line reported by the Times, Post and Tribune has much by way of corroborating evidence (e.g., see Nero Germanicus's listing at Post #48). One can't say the same for "moved to Indonesia at age 2."