I don't think that is the norm. If you can handle any black or double black with any snow condition, you are probably far better than any type of intermediate skier. On the other hand, skill level does not necessarily match the terrain you are comfortable on. You clearly are comfortable in difficult terrain, so you could join any group of students and not hold them back.
But there are many people with good techniques who could not handle the conditions you can. Lack of experience in that type of terrain, fear of exposed runs, fear of heights, fear of injury, age, can be overwhelming to some. Those skiers may see themselves as advanced skiers, even though this may not be fully deserved.
The best approach is to talk about both, skill level and terrain where you are comfortable.
To give you an example, I consider myself an advanced skier, but I could never pretend to be able to handle anything a mountain throws at me. Perhaps I should consider myself an intermediate, but I honestly don't think that reflects reality. Last year in Snowbird I remember following BobPeters and a few other into Mineral Basin. He took us to a great run (nothing scary), but the traverse seriously scared me. I think at one point AC even asked me if I was OK. The point is that I never get to ski in such exposed places, so my fear of heights really made it a scary traverse. Skiing in the East gives you lots of difficult terrain and conditions, but you rarely find yourself in exposed areas where a fall could be disastrous. One has to get used to that.