“...Toutonghi said her daughter asked if she had voted for President Obama because she had once baby-sat him.
“I said no...”
She wasn’t saying she didn’t vote for Obama.
She was saying the reason she voted for Obama is NOT because she had once baby-sat for him. In the original interview, at the end of the interview her comments make clear she is a supporter of Obama.
If your point is that you don’t believe anything she says about the baby-sitting because she is an Obama supporter, you can hold that opinion if you like. I don’t go that far, myself.