well Don, some things in life are never certain. So you go with known history, probability, past experience, observation and price.2: I would like to think I am in a safe boat and the captain cleared the crossing with the port authority, but how the hell do I know.
I know the op I dive with had his boat custom built from the ground up some years ago now and that he maintains it spotlessly. (I have sat on the prow, back in caleta after a trip watching the mate scrub down the entire surface with soapy water and a sc rub brush and all the cushions). This kind of care goes hand in hand with a desire for proper mechanical and other physical repair. that I have NEVER experienced any sort of mechanical difficulty on the water while on this boat would tend to bear this out. Second, I have seen and heard the captain call for permission to cross the channel. so I know it gets done. And I have seen him enforce marine park rules about knives, gloves etc so know he is a rule-abiding guy; he is most definitely not one who subscribes to the "we don't need no stinkin' rules" philosophy. Others may like the latter philosophy because it makes them feel in charge and a bit rebellious. Not me.
Finally, as Mike says, shoestring is as shoestring does. Others may feel they get better diving value for their dollars by going the cheapo route but I am not one of them. You may note that whenever I am recommending Jeremy's operation to someone on this board, I usually spend time talking about the boat in as much or greater detail than other aspects. I am so attached to his boat that when he has too many customers to fit on one boat, and is renting another, I will usually choose to go out on the Jewfish, regardless of who is DM or the skills of the divers on that boat. One exception I would make is the Sleeping Shark; I have been on it a few times and think it is nice and well maintained also. I think boats - and the comfort, safety, and convenience they afford - are a distinguishing feature among ops.
Now a newbie to Cozumel - or anywhere for that matter - does not have the advantage of having gone on hundreds and hundreds of dives with a single operator and craft. So they need to rely on the advice of people with like-minded expectations and desires. I think these are equally important questions to ask as how long they let you stay down, if the DMs are a fun bunch, what time they pick up etc etc. YMMV.