From rather religiously following FinalGear threads over the years, here's how I gather it works: BBC is the production company. They pre-sell the episodes in a block to History Channel, and have no idea who will advertise the show, because the production and delivery of the shows to History is done independently and in advance of History's advertising deals. For example, for this eight-episode season, they did the remote segments first, and finished up all the episodes with the "studio" segments. From following Rutledge Wood's twitter, you can see they filmed these "studio" segments, (the ones in the hanger with the audience) in December. So this Mustang segment was probably done well before that even. Even if an episode is sponsored by a car company, that sponsorship is done through History channel, not the production company, BBC Worldwide.
From what we've heard too, the BBC also gets final edit of their shows, not History, since TopGear is BBC's and they are very protective of the brand. Here's what the BBC's executive producer of Top Gear, John Helsing, said about it before Season One: "Not to disrespect other car shows, but they're fundamentally comprised," says Hesling. "They have to say the Prius 'handles like a NASCAR,' but Top Gear couldn't be like that... we will be absolutely and brutally honest. That's what Top Gear is."
Obviously, the BBC is very concerned about the perception of bias that comes with advertising, especially since such bias is illegal under the laws the BBC operates under in the UK. From everything I've heard about the production of the US show, I think the same BBC production mentality is present here as well.
You do realize that a ton of episodes of UK Top Gear aired on the BBC America channel here in the USA also come with the same types of tag lines like "this episode of TopGear sponsored by Toyota," or Ford, or Kia, or whatever too, don't you? Well they do. But I don't hear anyone saying that compromises TGUK's output. Because they don't.
The only legit concern I could see is the fact that Tanner has a factory ride from Ford when he's racing. But if you notice, most of the time so far on all the other episodes of this show, Tanner hasn't driven Fords. So I think it's apparent the producers are sensitive to that perception as well. In the muscle car segment, you'll also notice that Tanner was the one most vocal about pointing out what he believed were the problems with the Mustang's design, suspension, and motor placement, while he drove the Camaro.
What is TopGear supposed to do, pretend the Boss 302 isn't one of the best Mustangs ever just so people don't think there's a bias in case History manages to sell time to Ford, even after the episode is filmed and "in the can?"