Downstairs, Canton is still doing unspecified filing of paperwork (not knowing that Amy has solved/unsolved the case upstairs) and there's a scary knock at the door. Renfield goes to the door and has a hushed meeting with them, about which he refuses to tell Canton because he doesn't remember what just happened. Canton strides to the door, which opens of its own accord, so he clicks his palmcorder and asks the Silent to tell him what's going on so they can remember it later.
While Amy screams for help upstairs, the Silent goes, "This world is ours. We've ruled it since the wheel and the fire. We have no need of weapons." Canton shoots him, because he's American and that's what we do. Ha-ha! Americans shoot things.
You know what else? Nixon was paranoid and recorded everything, which was his downfall. I appreciate the concept of history being rewritten thanks to the Doctor -- it's kinda what the show's about -- and there's a certain small bit of elegance in having it happen here, when the paranoia is justified because of the Silence and when the recording thing is already established, but you know what would have been more elegant? Having the joke be something more than the Doctor literally saying, "You have to tape everything that happens in this office, every word, or you won't know if you're under the influence! You have to trust me and nobody else!" Because get it? Do you?
Also, when Nixon asks why he was fucking around with Apollo XI, the Doctor totally goes, "Think. Try to think." Like you're an idiot if you don't immediately grasp that the Doctor's going to kidnap an injured Silent and get it to say certain words in the correct order and then insert a subliminal command into the moon landing to cause a worldwide genocidal revolution that nobody will ever remember. Like duh, Dick!
Cue the anguished cries of Amy, on the other side of a door, when Rory and the Doctor join Canton and get the bedroom open. Except she's not there, the Spacesuit is empty... And the little girl is hiding down the hallway, breathing hard. Rory finds Amy's palm-transmitter, so we get to hear her freaking out on a one-way transmission that the team can hear. Wait, what? You're saying that's not what that thing is for? Don't be silly! "It defaults to Live. This is current. She can't hear you. I'm so sorry. It's one-way."