You still haven't answered the above question about what happened when you went to the front desk. Did you end up sleeping at the hotel?

Did you show them the reservation on your phone? Did you give them the confirmation reservation number?
Did they tell you there is nothing they can do and asked you to leave, thereby leaving you without anywhere to sleep for the night?

If you gave them your reservation number, they should have been able to look up the booking.
Once they established you had a genuine booking - and they were already fully booked - they needed to provide you with a night at another hotel with transport paid for by themselves - and they needed to pay for the room at the other hotel - and, if you were still very annoyed, refund your points.

If you didn't give them your reservation number, not much they could have done if they really couldn't find it any other way.

If you did give them your reservation number & they simply said they were full - then they have not followed the above policy which is, I believe, accurate although others here will know far more than me on that Refusing to move once they managed to establish you had booked a room; until they gave you a room *somewhere to sleep* would have been a start / escalating to manager.