One of the jobs of the Game Master is to keep the game on a steady keel when players start to argue about what to do. A bit of spirited discussion can be okay, especially if it's in character, but if it looks like things are turning into a real argument then one way to defuse the situation is to give the players something else to think about. Something more urgent. So that whatever courses of action they were arguing about become irrelevant, because none of them are going to address the new problem.
And in this way you can turn an argument over what to do about one thing into an argument over what to do about the new thing...
Commentary by memnarch (who has not seen the movie)
Looks like Pete has the same issue I do with the small number of fighters sent. Finn makes a good point with the hangar getting blown up, but at the same time, having only a single hangar seems odd to me. A single hangar for all of the available fighters might make sense for a small base, but this is a star destroyer here. At the very least, I'd expect a hangar on the port side and starboard side of the ship. And with the added benefit of outside universe knowledge, we can see that not even all of the fighters in this one were blown up, so we know that Finn's argument would have even less weight.
Unfortunately, I think Pete just holed his own argument about not bringing Finn along to the headquarters. Headquarters should be the best location to securely interview someone if the HQ is actually secure in the first place. There should be little to no room for unsecure transmissions or unauthorized equipment, and this isn't Star Trek where the main characters can turn stones into signaling equipment with a few hours time. And as for any concerns about Finn being tracked to the base, a spaceship is much easier to follow than a small human. The Falcon would already be trackable if Team First Order can track the ion signature or whatever can pick it up, so Rey & BB-8 would be in the same trouble as they are at the moment even if Finn gets dropped off on a planet or dumped into space.
And finally, this is why you don't want to intentionally damage the ship you're riding in too much; the risk of puns greatly increases. The ship might also explode under the pressure it was put under of course, but with proper ducting, the ship should at least give you a chance of survival. Letting off some steam smoke in a smaller bang like this is much better than bottling it up for a tragic outburst later. And this looks like the GM is giving Annie a chance to put a lid on Finn's cover again, which will definitely cause some outbursts when it blows for good.
Commentary by Keybounce (who has not seen the movie)
Rey is asking all the right questions. Makes sense, this is Pete. He's probably done all of these ideas in all the various what-if's he's done.
Why only two fighters? (Just like why only four in Episode IV). Where's this "Poe"? (Note that BB-8 can confirm the existence of Poe).
And Corey has the wonderful idea: Blindfold him. Which would do absolutely nothing.
And then, when the players are arguing, and nothing is going on, Have someone charge through the door with a gun drawn! Have a big smoke explosion to give the players something that has to be taken care of now.
Transcript
Rey: Also, they sent two measly fighters. Why not a squadron?
Finn: Poe and I blew up the hangar!
Rey: A likely story. And where’s this Poe to corroborate? Dead! Did you kill him?
Finn: What? No!
BB-8: Guys, guys. There’s a simple answer.
Rey: Yes?
BB-8: We take him to the base blindfolded.
Rey: It’s through hyperspace. He can’t see where we’re going anyway.
Finn: So just take me there!
GM: Suddenly:
[SFX]: Bang!
GM: Smoke pours out of the floor grilles.
BB-8: Phew. I thought that was Chandler’s Law again.
GM: No, I just wanted to vent.