I'd say that you can mix social in with physical because there's nothing stopping you from turning a social encounter physical. Seriously - can't we all picture:
Player: "He did how much social stress? Ouch. Okay, I'll take 'can't take the heat' as a moderate to soak up most of that, then I draw my gun and shoot him."
GM: "Huh? But..."
Player: "Yeah, I know he has those henchmen and there's that camera on the wall, but there's no way I'm going win this socially so I'm shooting him."
GM: "But this a social combat and..."
Player: "Gun. Him. Bang."
No GM would say you couldn't do that. For that matter, being taken out socially could mean being forced to attack someone when they have their henchmen around and camera recording everything.
So if someone can turn a social conflict into a physical one, why not at least allow them to try to turn a physical one social. Something like:
Player: "Damn, that's a big gun. Okay, so I'll take 'only a flesh wound (ouch)' as moderate, duck behind cover, and yell over 'Frank, I've got your kid'."
GM: "Huh?"
Player: "I can't take this guy physically so I want to do something social. Look, when we were staking him out we learned all about him and his family, right? So I'll use investigation to declare that I know his daughter's schedule and that she's on a field trip today so he can't contact her right away. I tell him we've got his little girl and if he doesn't drop the gun then maybe she's not coming home tonight. That's deceit, right?"
GM: "Um, isn't that a bad guy move? You're playing a hero and ..."
Player: "I'm playing a smart hero and I'm bluffing. Grabbing the kid, that's a bad guy move, but saying I have her? That's nothing. Maybe it will take an exchange or two but I might take this guy out socially. I sure as shit can't do it physically."
If that were to happen I'd do one of two things:
GM: "You can roll, but it won't work. He doesn't actually care for his family." (or maybe: "He yells back 'You can't have her - I just sacrificed her to the Dark Ones! Her blood tasted better than her mother's! Bwahahaha!'.")
or
GM: "Um, well, um, okay, next round I'll shift things around so your initiative order is your social one. Um, and you're doing some physical stuff, so -1 for combining skills, and he'll get to tag 'distracted by the gun fight', but go for it."
Player: "Cool! And next round I'll take out my cell phone and tag it. I'll say something something like 'She's safe now, but drop the gun or one word from me and they'll start beating her like a red headed stepchild.' and keep bluffing until he drops the gun or someone else brings him down. And I'll keep making new stuff up, stuff that he might believe. Saying we're going to kill an innocent kid is over the top but I can bluff about someone taking a belt to her - he should believe that. If nothing else I'll make him use a consequence or two for social stuff."
GM: "Um, you can't tag your cell phone and he won't see it because you're behind cover, but you could add it to the lie. Pointing out that you have a way to contact whoever has her can be part of the lie but the cell phone..."
Player: "Then I'll spend a FATE chip and declare that 'It looks like I'm talking to a psycho babysitter' and tag that. Maybe make something up about her. But that's next round. This round I roll and I get ..."
I mean, it's not like we are talking one second rounds. An exchange is an exchange and lasts long enough to do something simple. Yelling something in a firefight, that's something Harry might do.
Richard