I don't have strong feelings either way about the conclusion you arrive at, but I do have some questions that might at least partially explain the result, or at least be food for further discussion.

How many teams are unmanaged? It would be interesting to see a study of how those teams fare at home.
I have noticed with unmanaged teams that I have taken over that there is a tendency on the part of the robot to use players on unmanaged teams until they are overused or used up, while most human managers would presumably try to save their players by pulling them in games that are lopsided and against inferior pitching.

How effective are managers at setting their away pitching preferences and lineups? This could skew the results, though it would seem it would skew them in favor of the home teams. Maybe most of you are a lot smarter than me, but I'm constantly frustrated in trying to get things set so the robot will play my team the way I want it to on the road.

How many managed teams let the robot play some or all of their home games? And how do they fare, compared to the play of teams whose managers actually play the games?
All of this would be a lot of work to track down, but might create some interesting inferences related to your post.