I'd have been livid and would have said something while her, and the other doctor, were both there. That's absolute garbage and I would have refused to pay.
Coincidentally, the worst appointment I've ever had was with a dermatologist. I had a spot on my face that worried my wife (her mother has had skin cancer removed 2x). I called to schedule an appointment and they didn't have any for 6 weeks. That's fine, I get they're specialists and busy.
The morning of my appointment, they call me and tell me that they need to reschedule. No reason why, just "we need to reschedule your appointment". Guess what? They can't schedule me for 6 weeks out BUT they can keep my on the list to call if an appointment does open up. I'm a little frustrated by having to wait 6 more weeks (mostly because my wife is still worried) but I understand, things happen.
3 weeks later I get the call while I'm at work that they have a slot that just opened but it's only 20 minutes from now. I tell the admin that I'm 30 minutes away and there's no way I'd make it in 20. She says that would be OK, she'll slot me in and if I'm 10 minutes late, no big deal. Great! I fly out the door, call my boss and one of the managers that reports to me from the car to tell them both where I'm going AND let them know I'm going to miss meetings we have scheduled.
I show up to the office 24 minutes after I hung up the phone with the admin. She has me fill out some paperwork and then tells me to have a seat in the waiting room. 15 minutes later I'm brought to an exam room by a nurse, she asks me a few questions, why I'm there, yada yada, and eventually tells me to wait and the doctor will be in to see me in just a minute.
Another 10 minutes goes by and finally I hear the nurse and doctor outside the door. I can hear the nurse talking to the doctor about my spot, and then I hear something that really pisses me off. The doctor starts talking about me being "late", why I would even show up if I wasn't going to be here on time, and how she should just refuse to see me. It was all said in a super condescending tone, like I was inconveniencing her by being there. Once I heard that, I'm sure I had steam coming out of my ears.
Eventually, the doctor walks in and before she can say anything I tell her I heard everything that she said on the other side of the door. I explain to her that after waiting 6 weeks they called to reschedule me for another 6 week wait, that I then waiting 3 weeks and thought I was doing both of us a favor by filling in for an appointment that someone cancelled last minute, that I told her admin that I wouldn't make it there in time for the slot and was told it would be fine, and then to top it all off, waited 25 minutes before she decided to grace me with her presence.
You could see the "I ####ed up" in her eyes as she tried to backpedal and tell me the reason they had to reschedule was because of a burst pipe, while I put my coat on. I told her to cancel the appointment scheduled for 3 weeks from then and don't ever contact me about anything, ever, and then walked out.
I ended up scheduling an appointment at a place in Denver (about an hour drive from my house) and had a much better experience. The doc told me the spot was nothing to worry about but they could freeze it off if I wanted. I had it done just to please my wife and was in/out of the building in 45 minutes.