That's a delta mixer valve which is $100, plus $100 for the trim. A plumber would charge double for that, so $400 for parts. Usually labor is about the same as parts so I would expect that job to cost $800.
Maybe there was a lot of labor involved, or maybe he's embellishing the story a bit (or leaving out some of the work involved).
All the comments in the video have the same question as you.