No this is not necessarily true.
I picked arbitrary numbers out of the air to help illustrate a point, and you are debating those numbers instead of the point I was illustrating.
You then go onto support my point by giving different numbers and then agreeing with my point - i.e. that based on your personal knowledge of yourself, there is a depth where you expect narcosis to set in but lesser depths (40 feet) where you aren't concerned about it at all.