Yes, I've had this at the dentist.
Massive tailback on the way there so I rang and said I'm definately on my way but theres a big tailback on the road, receptionist said OK, we'll see you when you get here.
Got there half an hour late and apologised, said I was the one who had rang etc etc.
At the same time a man was at the desk asking when he was going to be seen as he had been waiting 45 minutes.
So, seeing as there was a 45 minute wait, technically I wasn't late.
Receptionist went to see dentist, who said No, I couldn't be seen as I hadn't turned up on time (even though I wouldn't have been seen at the correct time anyway).
Receptionist asked if I wanted to make another appointment....eeeer no!
Two weeks later I got a letter off the dentist telling me off blah blah blah for not turning up for an appointment!
Oh yes, I enjoyed replying to that letter, copying in the dentist, the practice manager and the local NHS manager.