There actually is a legitimate Putin comparison here. We need to remember that Hitler was Austrian. He did not regard Czechoslovakia, or much of the rest of Central Europe, as foreign soil. Hitler's prewar territorial demands were largely a matter of reassembling an historic confederation that had been disassembled at Versailles, but under German rather than Austro-Hungarian leadership.
I always recall the old joke about the world's best public relations coup: Austria convincing the rest of the world that Hitler was German and Mozart was Austrian.
If one was arguing where these individuals were born, this would be a funny line.
But Hitler most certainly renounced his Austrian citizenship and became a German national. In the eyes of the law, he was as German as any native German in the country.
Mozart was Austrian. The joke names Beethoven.