Nor has anything you said precludes it being a pre-refit version.
If another pre-refit version returned home during the refit of Enterprise, why would you start refitting it until the refit of Enterprise proved it could be done and was benefical? It could have been a year or so until the Enterprise refit was complete and the returning ship could have been older than the Enterprise at 25+ years so was nearing the end of it's operational life. So rather than expend resources on something that might not prove benefical the ship was simply decomissioned to the Fleet Museum.
Once the refit process had proven benefical it is possible that pre-refit ships returning after the completion of the Enterprise refit were refitted.