I was worried that by the end he would be hailed as Colin Baker, but for the duration of the show he was the Doctor maintaining the illusion. In fact, he didn't even get "outed" in the credits; only the appearance by some super-model (Jamie Kedd, I think?) was credited. It's a situation that reminded me of an episode of 'I Love Lucy' which guest-starred George Reeves as Superman. Mention of Superman was made in the closing credits, but not of Reeves.
So I'm willing to accept this reality show episode as a bona fide crossover with 'Doctor Who'. And that's despite the fact that Baker looked so much older than he was at the time of regeneration.
Fictional characters have appeared in reality shows in the past, but those have been as seen within the fictional setting of the other shows - 'Cops' in 'The X-Files', the U.S. 'Big Brother' in 'Yes, Dear', 'American Gladiator' in 'Family Matters', the U.K. 'Big Brother' in 'Dead Set' (found only in Earth Prime-Time_Zombie, along with 'The Walking Dead' and "Steve Niles' Remains".)
The reverse scenario of the fictional in reality shows? The only other example that comes to mind is Jiminy Glick appearing for the full hour of 'The Larry King Show' on CNN. Unfortunately, near the end of the show they did a segment on how Martin Short gets into make-up to play the butterball celebrity interviewer.
So why did the Doctor show up on 'Top Gear'? And why did he look older than when he "died"?
Addressing the aging issue first will help set up the rest.....
This Sixth Incarnation of the Doctor was not the one from Earth Prime-Time. He's the Doctor from the alternate dimension in which John Lumic created the Terran tinmen dubbed the Cybermen. But as we've seen happen in 'Star Trek' ("Mirror, Mirror") and 'Smallville' ("Luther"), when a TV character enters a new dimension without following the proper protocols, their doppelganger replaces them in the dimension of origin.
So when the Tenth Doctor, along with Mickey and Rose, crossed over into the "Over There" dimension (Yes, it's Walternate's world from 'Fringe'!), the current Doctor of that world was snapped back to Earth Prime-Time in his TARDIS.
But it wasn't a twin of Ten; it was a silver-haired Six.
Apparently, the dangers faced by the Doctor in that dimension weren't as deadly as in Earth Prime-Time. But then they didn't get any Cyberman threat from their version of the planet Mondas - their Cybermen were home-grown only recently. (Just as the Doctor of the Main Toobworld arrived.)
So the Sixth Incarnation of the Doctor didn't have any need to regenerate at the same time he did back in Earth Prime-Time. Instead, he was allowed to age naturally.
Now, the 'Doctor Who' episodes about that Cybermen world took place in 2006, while the 'Top Gear' guest shot preceded it by three years. Not a problem when your a Time Lord with a TARDIS. While he was on Earth Prime-Time for the two days of the exchange, this alternate Sixth Doctor used the TARDIS to go back and take care of a threat to Earth Prime-Time from his own dimension.
And we'll have more on that next.....