Under what authority does the U.S. military seize private property in a friendly foreign country?
Something strange is going on here.
As mentioned above the Status of Forces Agreement (SOFA) with Germany could allow this. Google or Bing or search engine you prefer - it's a binding agreement and explains how it works. I read it.
That said, who knows if it actually happened and what is still on those servers?
US Military does not need German permission. Germany is protected by US Military and has several bases in Germany.