If they charged me the day rate for that first 'night' I'd grudgingly accept their view. Is that what led to the different charge for one of the nights? In which case I'd tell them I'd like a room for day use and roll in from clubbing at 3am for a few hours kip to see if they honour the booking .

If I was told that I'd failed to check in for the first day and got charged a penalty I'd understand their twisted logic and argue with them.

If the reservation said 18-22 and I got charged 4 full night rates then I'd expect it to be treated as a 'normal' 4-night stay.