I'm not sure what videos you are referring to but I dive in Cozumel at least twice yearly and find the reefs absolutely beautiful.
Here is a link to a video I made last year covering over 15 dives across most the popular reefs. You can judge for yourself but I didn't see any of the algae you are referring to unless things have changed this year.
That's a very nice video. That is the sort of thing I was hoping to see. Most of the videos I had run across looked like yours does from 2:10-3:00 where there really aren't many corals. I was worried that was typical, but your video shows there is a lot more variety than what I was seeing elsewhere. Thanks for posting.