Everything you say is correct, but I also think people sometimes take away the wrong lesson from that dynamic, and that's what (IMHO) turns into the unhelpful "be yourself" advice.
That is, "When I'm funny/socially-adept, I'm [so unconsciously competent that I'm] not spending any effort to think about it. Therefore, if you spend no effort and relax, you will show the same skill. If you can't, you just weren't listening to my advice."
That is, "When I'm funny/socially-adept, I'm [so unconsciously competent that I'm] not spending any effort to think about it. Therefore, if you spend no effort and relax, you will show the same skill. If you can't, you just weren't listening to my advice."