The more I look through my players, I think fouling can be attributed to any (or a combination) of these skills:
Outside defense
Inside defense
Shot blocking
Stamina
Which is absolutely logical and was what I suggested a while ago.
Sorry I missed that, I've been monitoring this thread alongside the "Fouls" thread in the Help forum.
So using the players I posted above, I'll provide their OD, ID, SB, and Stamina.
Here are my players that foul a lot:
(2268579)Outside defense: average
Inside defense: mediocre
Shot blocking: atrocious
Stamina: inept
(2342139)Outside defense: average
Inside defense: pitiful
Shot blocking: respectable
Stamina: awful
(790523)Outside defense: atrocious
Inside defense: average
Shot blocking: mediocre
Stamina: mediocre
(2402768)Outside defense: respectable
Inside defense: mediocre
Shot blocking: pitiful
Stamina: respectable
And here are my players who nearly never foul:
(708999)Outside defense: awful
Inside defense: proficient
Shot blocking: atrocious
Stamina: average
(708995)Outside defense: respectable
Inside defense: proficient
Shot blocking: average
Stamina: respectable
(864174)Outside defense: awful
Inside defense: strong
Shot blocking: average
Stamina: proficient
(709000)Outside defense: respectable
Inside defense: proficient
Shot blocking: strong
Stamina: average
This makes me almost certain that fouls have a bit to do with the position of a player on the court and the skills of their opponent in collusion with their own skill set. So a player who fouls rather often in one position may not in another position (and vice versa).