Update: I just called the airline to ask them (United) and the rep read through the guidance that was just updated on June 2. She said their agents are trained to only look for two things: that the test type is correct (antigen in the case of BinaxNow Home Test), and that the result will not be older than 48 hrs upon arrival in Germany. They see lots of different certificates on a daily basis. Home tests are not specifically banned when performed under supervision. In fact, she said she knows there are testing services that go to the home of the passenger to deliver a kit and again to pick it up.