Maybe you just haven't met the right people. I definitely "just do it" all the time. When I needed to develop a single page app for the first time, I just did it. When I found I needed to automate server deployments, I just did it. When a project I told someone I'd prototype needed me to design a circuit, fabricate a PCB, build it by hand and write firmware for its ARM microcontroller (including an OS), I just did it. And had fun doing it.

I'm sticking with my "full stack" claim. I think I've earned it.