It implies that they had to 'piece together' that body, or that not all of it is there.
I don't think so...
I just looked it up and "remains" means "a corpse".
No, it implies that the physical body is all that REMAINS of President Reagan, at least in our world. It implies that the dead body isn't President Reagan, that his soul has left his body, and hence his body is what remains--at least physically. It's not a term of disrespect. In fact, it suggests the contrary--that his soul lives on. It doesn't imply that part of his body isn't there, only that part of President Reagan isn't there. And there's no denying that.