I'd say this characterization is questionable at best. He worked as an engineer for 4 years and then got a Ph.D. in Physics, as well as working the majority of his life as a physics researcher and teacher. It's like calling a surgeon with an undergraduate degree in Biology a "biologist'.
Well there's also the fact that the transistor is an applied physics device and not really the discovery of any new fundamental force or particle. Which some would (wrongly, in my opinion) consider engineering.
Wait, why are these things mutually exclusive? He was both a physicist and an engineer! He literally used his knowledge of physics to physically engineer novel devices.
As for your surgeon example, I sure as hell hope my surgeon identifies as a biologist. If someone's slicing me open, they better be up-to-date and involved with the literature. (To your point, after speaking to my fair share of medical doctors, it seems a frightening few actually do this.)
