True, She could have been decommissioned in 2161 but with the refit hull, that wasn't represented on the Horrible TATV.Whether the program was historically accurate or not, the fact is that Kirk's ship was supposed to be the first Federation starship Enterprise. Therefore they had to decommission the NX-01 before the formation of the Federation. So either the holoprogram was accurate, or the ship was used as a non-Starfleet, non-Federation ship after 2161.
I'll go with she was refited for the Romulan War, and the events depicted in TATV were some persons depictions in a Holo Novel that they cooked up like a Romance Novel.