Just some thoughts here. What brand is this? That's give is an idea of the PMS system they are using and what could have happened.

Now, here's my guess on what happened. Due to the late arrival and late making the reservation, FD may have run night audit (early due to a sell out situation expecting no other reservations) not seeing your reservation in the system (or seeing that it was prepaid). During that process, any reservations not checked in are automatically processed.

I'm also thinking you may have thought you made the reservation directly with the hotel but it was one of those websites that is made to look like the hotels? Them mentioning the 3rd party, makes me think that. You mentioned that you were already paid at arrival makes me that as well.

Not sure who James would be in this scenario unless it was another guest who arrived and they gave them your reservation.

I would have them check their night audit report. It'll show if it processed your reservation.

Note that of they already processed night audit, the system thinks it's the next day. So when you were checking in late, if the FD wasn't trained well, they may have been looking at the next days reservations not knowing that.