You are partially technically correct, except for the minor detail that the native tribes who probably hunted most of the American megafauna to extinction didn't believe in "Manifest Destiny" per se. The reason there were so much buffalo around when Europeans showed up was because all of their typical predators had been killed off a long time ago.

Also, as far as I can tell from the limited research I care to do, there has never been a rhino species native to the New World.

So to answer your question - there were probably never any white rhinos in America to begin with, and had there been, the Americans who would have killed them are not the Americans you seem to be referring to.