The whole point of this thread is not a cave diver vs the wreck diver it is about certifications and diving within the limits of the your certifications. If you don't have a card that says you are certified for a specific type of diving then you are not certified for that type of diving.
Similarly just because you have a certain level of certification does not mean that you automatically have the certification to make dives that appear to be of a subordinate or comparible level.
A brain surgeon is not certified to perform open heart surgery, he has an understanding of the human body but his specialty is the brain not the heart.
A pilot of a cessna understands principles of flight but he is not rated to pilot an airbus.
Now do we need a card for each and every type of diving out there? NO and NOR Am I suggesting that and nor am I afixated on needing cards for everything. I would like to think that a responsible cave diver or any diver as may matter would understand and be respective to the instructors point of view, those who may have an ego would not fit into this category of course. The fact that many charters do not appear to worry about what certifications a diver has short of looking at c-cards and simply lets them go off and dive is irrelevent. They accept that risk and expect the diver to stay within their limitations. The diver themselves must also accept the risks of the type of diving they are about to undergo. And yes they should have a full understanding of what the charter would let them do before booking it. If you think a charter doesn't care then watch and see how they respond and think when something goes wrong?
There are a copious amount of certifications out there and it is not realistic to think that you could hold each and every one of them. Like many new instructors I went and got as many instructor certs that I could teach as possible. Today I look at some of them and think they are rather mute, others I do not.
Example: I would not stop a diver from getting on a charter because he was lacking a Boat Diver Certification but then I would not just let a cave or wreck diver join me on a ice dive.
We say that the card does not matter, we say that it's all about the experience and training a diver has. Well the c-card is a Diploma of that training illustrating that the holder has successfully completed the standards required of the agency for that certification level having followed a prescribed course and passing some form of examination and skills confirmation. The c-card at the very least will represent a degree of knowledge, observation will prove their skill. The c-card does represent training a diver has undergone, it is the level of thoroughness and quality of training itself that is subject. The instructor in the example of the first post is right to make the "no dive" call for this and for reasons of liability.
For what it is worth for those who do not know me, I am a Cave, Wreck and Ice diving instructor (whoopie). They are all overhead environments and I can see the differences in the environments and certifications. OOPs my ego and arrogance just got the best of me... so sorry!