Actually, I wonder about that, too. I also wonder about his companion. Had the other guy already left by the time the police got there? When asked if there was anyone else in the house (a routine question), Gates told them it was none of their business.
Personally, I think this was intended as a distraction to make the cop overlook something else.
After Gates’ trip to China, he didn’t come directly from the airport home to Cambridge. IIRC, Gates came from New Jersey where he had supposedly stayed the night in a hotel. Why didn’t he just go home from the airport? Just asking.