...The question of whether an instructor can write a test question and make it a requirement for certification is not central to the issue, and therefore it's an invalid focus for the discussion.
It definitely is relevant and you continue to evade answering my questions (we both know why). Considering that there are other threads in-which it's more appropriate to discuss Agency differences, I'll try to reconstruct what I've already said in-light of this thread. So I'll restart...
Not all Diver training courses are the same. Each certification Agency either restricts or encourages their Instructors to surpass training Standards. So regardless if a person trains in warm or cold water, the scope of the diver training program will vary (dependent on the Agency and the Instructor giving the course). This is a factor when you compare Diver competence; as some programs are much more comprehensive than another. In the context of the OP, it is a factor for consideration.
As to warm and cold water, it has been my experience that cold water courses (especially those that require the Diver to deal with tide, altitude, low visibility, current, waves and surf) require a higher level of fitness and performance than many vacation type courses that are undertaken in "ideal conditions."
I believe that any Diver Training Program should prepare the Student for the environment in-which they will dive locally. Moreover "Better Conditions" are those which have less environmental hazard. It is for this reason why a Diver who's certified to dive the North Atlantic (for example) is also certified to dive in ideal conditions. On the other hand, the Diver who was certified to dive in ideal conditions is not certified to dive in the North Atlantic (worse conditions). This is an understanding that's shared by all certification agencies. Generally, the "scope of certification" of a cold water diver is larger than that of a warm water diver; enough said.