You're right about the Silents, but that's not what I was talking about. The Doctor faked his own death, and Amy's sad because she'll never see him again, and he's "keeping a low profile". When you've woven a loud presence through space and time for centuries, stopping doesn't make it go quiet, it's still there, unless you rewrite your own history.
The Doctor's life has a sequence of regenerations, a beginning, a middle and an end, but only he and other Time Lords experience it that way. Even if he had died in 2011, it didn't stop him popping up in 20011, so from the perspective of anyone who isn't a Time Lord (or a tv viewer), the Doctor's death and birth would be abstract notions separate from the ever constant persistence of his appearance.