Somewhere between A and B. Naruto thinking Sakura still doesn't love him will make it all the more dramatic when he finds out that isn't the case.
I think he told his dad that Sakura was his girlfriend because he really wanted him to think so. He hesitated because he knew he was telling a lie and that Sakura would probably react the way she did.
I agree with Pepsi, I think he said she was more or less his girlfrien because he considers her as hs girlfriend when she's not really his girlfriend.