Yeah, something's wrong alright.

Just tried the same code I posted above (except I fixed the bit on line 8 where I had a typo in the trigger name) with an EventTrigger whose Root Template I changed to a Boxtrigger.
This is what happens:
As the character enters the first time (and doesn't exit).
Character gets the Burning status, then the Petrified status.
If the Petrified status fired while the character is still in the trigger, that means it is now unregistered... apparently.

Character leaves trigger.
Petrified status is applied again.

Character re-enters trigger.
Burning Status is applied again, Petrified status is not applied again.

Character re-exits status.
Petrified status is applied again.

So far, the code appears to work as expected for a normal Boxtrigger.
So I suppose the lesson is that EventTriggers can be Unregistered, but fire events even if they are?