Because your premise about "reasonably literate" is not well founded.
I have observed dozens, maybe hundreds of cases...
And as @summer notes, the State of Georgia is not bound by the federal definition of a shotgun, just like it has a different definition of "firearm."
Okay, I'll give you the fact that some cops just aren't that good at reading the law and knowing what it means and how to apply it in real life situations. I just read a case about that where a cop blatantly misinterpreted the law about vehicles having to have rear-facing mirrors, and the Court of Appeals said that his traffic stop of a driver was an unconstitutional and unauthorized seizure because the 2 side mirrors he had fully complied with the law, making that missing center-of-windshield rear view mirror (which was missing) unnecessary under Ga. motor vehicle equipment laws. The cop was sure that the law had to be read to require that all 3 mirrors be intact and working, or it was a violation.
HOWEVER, what's your second point again about Georgia not being bound by federal definitions of terms like "firearm" and "shotgun"? That's true, but irrelevant because Ga Code 16-11-121 has its own definition of a shotgun, which does not rely on the term "firearm," although the same concept is incorporated into the definition of both "sawed off rifle" and "shotgun" (and therefore, also "sawed off shotgun" by extension). Georgia law says shotguns are guns that are intended or designed, or redesigned, to use shoulder stocks. That's it. Nobody needs to ask ATF how they'd interpret that. Georgia law stands on its own.