Similar thing happened to me at a job interview back in 1997.
Appointment was at 2pm. I arrived at 1.45 and was directed to a chair in reception. At 2.30 the guy turned up. His first words were "you are late"
Sensing that this 'may' have been a test of some sort I apologised. I got the job and got to know the guy fairly well over the ensuing years. He did admit that it was a test of my reactions to unfair situations.
That happened to me when i was signing on at the Job Centre years back.
My signing time was 1pm, i was there at 12:50, my advisor had people at her desk all the way through to 1:20. I'd spoken to one of the guards and one of the other advisors telling them i'd been sitting for half an hour.
She gets up, goes away for 10 minutes, at 1:30 she comes back, calls my name and i go over, sit down expecting "i'm really sorry, we're miles behind today"
What did i get?
"Why are you late? your appointment was at 1"
I politely told he i've been sitting for 40 minutes, i was here 10 minutes early, she has had people at her desk then disappeared at 1:20 and i'd been kept waiting.
She then tried to tell me the only reason she was seeing these people was because i wasn't there and accused me of lying and just showing up now
I then pointed out that her version of events was impossible given i could describe the people she'd seen and the fact i knew she'd got up and walked away for 10 minutes, had spoken to the guard and another advisor in between times.
She went and spoke to the advisor and i could see them nodding and pointing where i was sitting...i expect then she'd apologise.
Nope, she sits down and says i'm getting an official warning for time keeping, "Why? it's you that's late?"
Her next angle of attack was how i was dressed, jeans, t-shirt and jumper.... "You should be wearing a suit, if you don't treat signing on as a job interview, you're not signing, that and your time keeping shows you aren't taking this seriously".
I laughed and asked if she was actually being serious now, she was, she refused to let me sign and said i was getting sanctioned with a right to appeal. Laughed, got up and told her to fuck off, went straight to the other advisor who'd just told her i was telling the truth and about the suit thing and they shook their head and basically said "oh ffs, she's on one again, give me your details and i'll note it" He signed me and said to just bring any letters i receive in next time and they'd wipe it off as a Job center error. Which is what happened.
Oddly that advisor was never seen again. Either quit or was sacked.