Only natives have the right to deny immigrants is that true for native Europeans?

That's not true for any nation. 

You 'constantly hear' nothing of the sort.  The earliest inhabitants of Europe were long ago killed off by successive waves of migrants.  Even the Celtic farmers of the Outer Hebrides and the Sámi of Northern Norway were not the first settlers of those places.  Governments make immigration policy not extinct populations of neolithics. 

Most native Americans who are still here --- are only here because their ancestors  killed off the tribes that came before them ?.

Even in the mid 19th century the Sioux were feared by other native American tribes for their ruthlessness.