Yep,
you're spot on. There are too many variables per game.
On the balance of probabilities and all things being equal the foul count per team should be rougly the same.
The actual number of fouls awarded per game doesn't matter and I think it's good to generate a manageable foul count - shows the players are working hard for the ball.
However, you miss my point. Human nature is that we find it easier to be nastier to people we don't know, or don't like, or who we pre-conceived ideas about. That's why prison officers and the like remove themselves emotionally from the sitution.
As a ref it is the same. If you are associated with a team, your natural instinct is to provide that team with a little more leeway than you would the opposition team who you don't know. If you had to shoot someone or be shot and were asked to shoot either a man you knew, or someone you didn't, you would select the person you didn't know each time.
You expect to get harder calls away from your home court. Look at the scoresheets for your team. I would expect that the team gets a couple more fouls on average away from home, but a few less at home meaning an overall a standard "bell shaped" distribution would occur. 75% of the time, you'll be within 1 std deviation of the average, and 95% of the time within 3 std devs.
When you are outside this range, then statistically speaking an additional factor(s) is at play,