Yeah, he said, "Is Rudy thinking of moving?" so I hit the Home button and closed the game without saving (by pushing the X button; I have been told you have to do this before his dialog concludes, so don't hit anything but Home when he gives a name). I then went back to the camp and went through all of the dialog again until he agreed to move in and this time he picked Renee. I wouldn't mind her going, but I needed the peppy to go. So, I tried a third time and got lucky and he said Bubbles.
I honestly don't know what would happen if I answered no when he asked if Rudy was thinking of moving. Maybe I then couldn't have him move in? Or maybe he'd insist on kicking out Rudy? I didn't stick around to find out.
I hope this makes sense.