In that particular situation, I rolled a +7 empathy roll. The GM said, "you know what, you fail that role - here's a fate point - I'm compelling your corrupt cop aspect. You get that he's telling the truth, but he's insulted you're insinuating he's corrupt. You just made an enemy on the force"
I think that's a really cool Compel, but it's independent from the Empathy roll. Since there wasn't an interesting way to "succeed", I would have just skipped the roll and gone right to the Compel.
As for full-out social combat, I'd only start that if both sides wanted something from the other person. In this case, if the cop thought it was
really important that you believed him, then a social combat would be useful. But if he didn't really care, then it's just an opposed roll. And in either case, I'd skip the rolls entirely unless both potential outcomes were interesting.
Technically, since I failed, he still could be guilty, but is using deceit. So we could have broke it all down into a combat, but it didn't really matter in the end. Could that same result have happened in a full-out combat? At what point does the DM say, "here's a fate point - you lose"
I think that compels can be done at any time, so a GM
could end a combat with a Compel. The only question would be why the GM started the combat in the first place if they knew they wanted a specific outcome? But maybe (a) they didn't think of the cool Compel until half-way through the combat, or (b) something happened during the fight that inspired the Compel.