OK, I think I've finally nailed the problem... Stylists are loading idols that are at their stat cap and trying to raise a stat that cannot be raised.
I don't think that's true. My training max was set to 20, the idols stat cap was 20, and the displayed stat was 20. So, if they were reading and reacting to the potential stat... wouldn't they have trained once (raising the hidden stat to 21) and quit? (Instead of constantly reloading the idol and training the same stat in an endless loop).