If you reserve and pay for a Private Room to sleep in, and they didn't give you a Private Room (and I wouldn't be able to sleep if someone came in during the night, even if I bolted the door and put the dresser up against it afterward), then you shouldn't have to pay for it.
Many years ago I checked into a low-budget hotel with a friend. Left our bags, went out for dinner and some drinks, got back to our room around 11:30. Opened door, there were other people asleep in the bed. Our bags were still there, so we apologized, grabbed our bags, and went to the front desk. Only room available was a suite, so we gladly headed there. Could hear the other guests we had disturbed shouting at the front desk from that suite, though.