“His parents immigrated to the U.S. seven years before he was born. They could have naturalized.”
They didn’t. According to the 1930 Census, they were both still aliens (and Mike was born in May 1930).
So yes, the FEC gave matching funds to a guy born to TWO British citizens.
Let's see the entry in the 1930 census. IIUC, the census would have been taken before Maurice was born, so technically they had time to naturalize before he was born. And again, this doesn't mean the FEC didn't accept any voluntarily submitted evidence, such as a legal birth certificate, something Obama may have opted not to take a chance on.