I concur with your reasoning. Further examples:
I can throw a football, but I'm not a quarterback.
I can prepare a meal, but I'm not a chef.
I can change the oil on my truck, but I'm not a mechanic.
I'm most definitely a drummer though.
I don't believe someone is a drummer simply because he or she can sit behind a kit and hold a basic beat, just as someone isn't a physician simply because he or she can apply a bandage to a minor cut. Drumming, like any other undertaking, requires commitment and hard-earned proficiency. When a band is searching for a drummer, a certain degree of know-how is a prerequisite. Yes, skill levels will vary, but a demonstration of competence and a willingness to take the instrument seriously should be a universal trait.