Look at it that way: If i die now and austria gets run over by germany after my death, for example, i wouldn't want to be considered german.
People consider Mozart as an Austrian, because Salzburg is no longer independent. There is nothing wrong with that, even if it is not historically correct. The same mistakes are made with Gandhi (as Indian), Leonardo da Vinci (as Italian) or Confucius (as Chinese).
"Adolf Hitler (20 April 1889 – 30 April 1945) was an Austrian-born German politician who was the leader of the Nazi Party (NSDAP...."