Communists claimed credit, btw. "Burned" = Molotov cocktails, "killed" = apparent smoke inhalation, given the carbonized state of the found body.
It’s been said that it was former members of the French Resistance that did in Peiper...”signs” (like graffiti in front of his driveway reading “A MURDERER LIVES HERE”) were out there for months after he moved back to France in the early 70s, and his (open) presence became known.
As to the “we forgave the Germans awful fast” comment, consider the fate of the Japanese scientists of Unit 731, which committed experiments in Manchuria that might have made Mengele cringe...MacArthur gave the chief scientists clemency in exchange for all of their data.