No you aren't. Again what part of "certified diver" do you fail to comprehend? What part of the assumption of risk agreement where signatories agree to check their equipment did you forget to read?
String, the assumption of risk agreement does not obsolve the operator from gross negligence in many (perhaps most) US jurisdictions. Any action that a dive professional takes on as part of their paid services will be scrutinized under "duty of care," and if it was the action of a reasonably prudent dive professional. No reasonably prudent dive professional would send someone underwater without the air turned on. Indeed, it is such an important point that we specifically go over in class how to do it multiple times, we have acronyms around making sure our buddies check it, and it appears in the OW checkout dives no less than 4 times.
It is not a stretch of the imagination to conclude that with such a heightened level of attention to that one item, failing to turn on air is in fact gross negligence.
To presume that the assumption of risk and other releases save the dive operator from legal action is simply failing to appreciate that those pieces of paper are not licenses to do any idiot thing we feel like doing. They offer protection but it is rare that they are a blanket cover for liability. Indeed, the discussion at that point becomes "ok, you admit the facts of the case, so you admit you would be liable, but you have a piece of paper you are holding up that you believe makes you bullet proof."
In some cases that will wash. But the difference between negligence and gross negligence is not easy to judge for those of us who aren't legally trained. It's the difference between a fool and a damn fool. If something like the OPs story resulted in a death the insurance carrier would be trying to settle the case as soon as the facts were known because the expense of trying to make the argument that denying a customer air while under water through inattention to simple detail is not gross negligence isn't going to be an argument they will be willing to make on your behalf.
Setting up gear aside (i think its a very very bad thing, encourages laziness) you have no liability. The DIVER is responsible for checking his own equipment and conducting the dive with it. Nobody else.
Then don't offer it as a service on your boat.
Again what part of "certified diver" do you fail to comprehend? They have forms, cards and signatures stating they are able to do it themselves. They sign forms stating they WILL do it themselves. Its not gross negligence. Its not negligence at all. Its utter stupidity from the diver concerned but nothing else.
What the diver said they will or won't do has no bearing on the responsibility of the DM to the diver when the DM is setting up the gear. If the DM is giving instructions to violate the training, the customer certainly should, as responsible well trained divers, tell the DM to go soak his head. However, in the real world, the customer will defer to the DM most of the time. The law tends to recognize human behavior in cases like this. And juries certainly do.
So the divers themselves were bot cavalier and negligent. Not the DM. They're supposed to be qualified yet they completely ignored their training and as such are diving outside the conditions of their training. That's nobodies fault but their own.
This doesn't change anything. There can be shared liability. But to say there is not negligence is foolish. To argue that it is not gross negligence is a reach. At which point what matters is entirely a matter of if you use a release to sign away liability incurred from gross negligence. In my location, that is simply not allowed.