I've done hundreds of dives with Deep Blue over the years and don't do any cheerleading unless they make sense for the person asking. For instance, they leave from a downtown pier at about 9am. If you stay downtown and don't want to rush getting on a boat, they're a great choice. Same with cruise ship divers. Deep Blue has been around for a long time and they have multiple boats (3?). They won some kind of service award a few years ago. They have good DMs and dive instructors. Since you're a one day diver, you'll be on the non-advanced boat, which simply means you won't go to advanced sites. I read a post awhile back where it was suggested that one day divers, or cruise ship divers aren't taken to the "good" reefs. Certainly not the case with Deep Blue. For the SI, you'll get water and fruit, and you'll either go to a beach club (Paradise) or to the dock in the jungle. Small, fast, covered boats. You'll probably be on the Pegasus, which holds about 10 divers, but there will be multiple DMs.
Don't be fooled into thinking that the aforementioned "top ten list", is a list of the top 10 dive operators on Cozumel, or that a shop not on that list is somehow inferior. It's more appropriately a list of the dive ops with the most vocal cheerleaders and has nothing to do with being "the best". As you've read, one of those shops has already been discounted by someone that was diving with them.
I've only been diving with 4 ops on Cozumel. One of them is on the list above and likely not the shop that was discounted by the other poster. In the week I dove with them, the shop wasn't bad, but I'd rather dive with Deep Blue, or another one of the shops I've experienced, which also didn't make "the list".