According to the White House, Obama did pay for the meal out of his own pocket, not any government funds. Of course, given history, we can't necessarily believe this, but no evidence has as yet been offered to the contrary.
The argument that because we pay his salary that everything he spends is really us spending it doesn't fly. Once we pay his salary, it's his to do with as he pleases, just as anyone else is. I don't hold an employer accountable for the personal spending decision of his employees.
“According to the White House...” Barry paid out of his own pocket. If that works for you, okay. I’ve been lied to so many times from that source that I no longer believe a word they say.