Because women can't drive, it's hilarious and faux-empowering that River Song can not only hush the TARDIS engines but put "the outer shell on Invisible," because you'd expect that she wouldn't be able to work the TARDIS but in fact she works it better than the male that usually operates it, so you see that's a subversion of expectation which is after all the root of most comedy. Women, am I right?
"You can turn the TARDIS invisible?" the Ponds ask wonderingly, having missed out -- much like the script itself, it seems -- on the whole thing about how TARDISes can look like anything whatsoever when they're working right. More made-up details about how the TARDIS works when she's "cloaked," while in the Oval Office Nixon plays a recording for Canton:
Mr. President? I'm scared, Mr. President. I'm scared of the Spaceman..." They talk about how it's not a little girl, but a little boy -- another strange detail we'll probably but not necessarily be revisiting, since it's a little girl in the end -- and the kid says her name is Jefferson Adams Hamilton before hanging up. Nixon explains that he's come to Canton because he gets the calls absolutely anywhere he goes, and that he can't trust the FBI.
(Running with the sub-elementary school understanding of history in which this show seems to revel, Nixon's paranoia and tendency to record conversations are mentioned hilariously in every scene, not unlike a cruddy Saturday Night Live sketch about a famous historical figure. Ditto the same joke, approximately twelve times in this episode, about how Americans shoot things all the time. With those guns we love so much.)
The Doctor suddenly appears in the Oval Office, while the rest of the team stays on the cloaked TARDIS, and there's all kinds of American chaos, and River keeps saying she hates the Doctor so he can smile and say she doesn't hate him, and they discuss how "Jefferson" is, in fact, a little girl, and the Doctor sasses everybody without actually saying anything for approximately ten minutes. Canton proves his worth by pointing out obvious things that get us over the narrative obstacles -- "Mr. President, that man walked in here with a big blue box and three of his friends, and that's the man he walked past. One of them's worth listening to" -- so... Now we like Canton!
It's really that easy, when your viewers have huge parts of their identity wrapped up in loving a forty-year-old franchise regardless of the quality on any given day. When loving Doctor Who is more important than actually watching Doctor Who, it's just that easy: Make sure somebody shit-talks authority while clearing the Doctor's path, and you know he'll end up a hero. Or at least onscreen, for a long time, without ever developing a personality of any kind.