"Random?" He asked, his voice rising as it often would when something was completely unbelievable. "Random?!" He asked again, giving her a look like, perhaps, she'd just grown six heads. "Come now River Song." He almost chided her with his tones. "I'm over nine hundred years old, you've seen me, you've traveled with me - an I'll assume you've done so a very, very, long time. When have you ever known anything in my life to be random - and the screwdriver doesn't count. Just because neither of us know why I gave it to you now..." He lied. "Doesn't mean it won't have a purpose later."
He was pacing around the TARDIS controls, watching her while she worked and he spoke. "Think-think-think-think-think. Got to think. Can't be a coincidence, too simple, too easy, nothing's ever that easy. No. Can't be." And then she spoke again, and The Doctor's eyes lit up like Christmas trees. "Ohhh YES!" He was practically bouncing around the TARDIS.
"Think about it. Time Lords. TARDIS. Travel all around the Galaxy, all throughout space and time, popping in and out where ever they like - zipping through the time stream all wooosh and bang! Drops out of the time stream, but where? Not just anywhere. A fixed point. It's why time flows so strangely around everyone here, even you. Not supposed to be here..." His voice trailed again.
"Then why so simple? Why so basic? Who so...American? Even with the great big, shiny, city, right next door, this place is remarkably quiet. Too quiet." It seemed The Doctor had found another hole in their theories, but they were making progress and that was better than nothing at all.