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.
Technically you're right, but there are implications to using certain words in certain contexts.
There's a newer term, "cremains" for "cremated" remains which I find to be a bit tacky. But my understanding is that "Remains" is ok... better than corpse. Body is ok too. Can't really think of anything else to call it.