As a diver, irrelevant that I am an instructor, whenever any of your "spidey senses" go off listen to them. There is a reason that we all were taught to be self sufficient, to a certain degree, and be aware of what is going on with anyone in your group. If you think that the person is blowing smoke up your a** and do not demonstrate proficient skills for a particular dive or trip then it is your responsibility to say NO! Whether or not they heed your warning is another matter, but at least you can remove yourself from being potentially being drawn into a lawsuit after that diver dies.
Ok my personal experience with this. Right after High School (2007,2008) for two consecutive summers I worked on Catalina Island as a dive master and instructor. It was almost a daily occurrence that I would be approached by tourists to the island about wanting to dive either off the dive boat or dive park. As a side note, IMO Catalina is the EASIEST "Cold Water" diving out there, whether boat or dive park. However, the first question I learned to ask was, have you ever been in cold water? While this question is relative to the person let me elaborate, has that person worn a 7mm suit, boots, gloves, and a hood? If they have not, generally speaking they will not be prepared to dive in cold water or at least they will have generally more anxiety because of the intensive use of exposure protection in comparison to tropical diving. As a follow up question, I ask where they were certified, how long their class was, have they done any dives on their own after their open water class? From this you can typically deduce what experience they have and possibly whether or not they will be mentally fit for a "cold water" dive.
To the OP, it is not that uncommon especially in destination diving to have people that are "certified" to not know how to set up gear and so on. It is shameful that many instructors in tropical destinations, who only deal with students that want a scuba "crash course" cause its a bucket list thing for them, not something to take seriously. It is not necessarily the fault of the instructor in this situation, but that of the industry who sets these very low standards. The instructor who probably wants to train the students better, is being pressured by the shop who wants to make the money to do it quickly and pressured by the clients that want to have the quick course. This is where the problem lies, if the instructor was to stand on principle in this situation he will lose the business, most likely, since those perspective students will just walk to the next shop that will do the certification in the time frame they want and the instructor will be be out of a job because now he is turning business away from the shop. It is a very simple solution to a very complex problem, the agencies want to make money that is a given, however the educators need to get together and demand that every agency require a higher level of competency and skill set by the OW students. There needs to be a standard set for ALL agencies in regards to time in classroom, time in pool, and time in open water. If we could accomplish this, I am well aware a lofty goal, then we would be able to get rid of this issue of incompetent divers who think they know what they are doing, so a confident moron, recipe for disaster! I completely understand that if someone was living in Hawaii and learned to dive there wanted to come to the West Coast and do some diving but were educated that it is a different style of diving and requires a slightly different skill set, we would obviously take the time to show them the difference but that generally is not going to be….here is your gear see you in an hour!
Ok I will get off my soapbox. I am not trying to offend anyone with this, just personal experience and personal issues with the agencies as a whole. The OP or any of us would like to try and get away from ill prepared students whom think that because their card says Advanced on it, they can do and go wherever they want.