A lot of simple songs are just open "cowboy" chords for sure. But those are played on the first frets while the guitar is typically intonated at the 12th fret and tuned with open strings. I would expect those first frets to be fairly "out" vs. the open strings.

“Whole neck” is irrelevant. Things can go out of tune at any fret.

EVH famously tuned his B string slightly flat to make his D (on the 3rd fret) sound better. Look it up.