You're also a bit at the whim of how the front desk decides to post it. I've had a lot of EEO's, HPR's, and other 3-for-2 type deals simply post as one or two nights. Either the "free" night simply isn't anywhere on the bill or it's there and completely adjusted off, leaving only the paid nights showing as EQN.

I've never been in a situation where I needed the nights to post in order to hit a status or Megabonus, so I've never argued. I don't know what official Marriott training protocol says the clerks should be doing. I would imagine that the intent is that the "free" night is not an EQN.