Continuing to pay close attention to this, and:
- It does not occur at the start of battle, but generally increases in probability the longer a battle goes on – until it’s occurring to literally every Troop every turn.
- It does not seem to occur to Troops with freshly-inflicted Status Effects, but when it does, the Troop gets cleansed.
That’s why it looks like it’s just the auto-cleanse chance, except now it’s occurring regardless of whether or not they even have a Status Effect at all.
I’ve seen it trigger on a Poisoned troop, but the Poison stays in place.