Fret buzz is not only not necessarily bad, but actually a part of the guitar tone. The guitar is partially a percussive instrument, and one percussive aspect of that (in addition to knocking or tapping on the body of an acoustic guitar or hollow-body electric) is the snap produced by string-on-fret action. Slap guitar technique in particular exploits this way of producing a sound. Aggressive "Rasgueado" strumming in Flamenco also exploits the percussive noise of strings hitting frets.
Is either of the following considered a poorly setup string action:
a) The strings buzz quite consistently but not enough to be heard through an amp or,
b) The strings buzz only if you pick the string quite hard and you can bend the strings without any buzz or fretting out.
These statements aren't wrong. The important thing is for the buzz to be approximately the same everywhere, hinted at by your (a). If you lower the action, and you get buzzing on all the frets at the same time in any given general area of the neck, across all strings, that indicates good setup. How much buzz you allow is an artistic decision. There is an objective "too much", when you can't produce a tone at all.
Uneven buzz is bad, indicating that a fret is not properly seated, or there is uneven fret wear that requires leveling.
Regarding (b): whether you can bend a string without buzzing out depends a lot on the radius of the fingerboard. This is why "shred" guitars have flatter radii, and why the "compound radius" became popular in the 1980's, whereby the fingerboard is basically the section of a cone (tighter radius at the nut, wider at the body). With the compound radius, the guitar has some of the characteristics of a Fender Stratocaster for chording in the low positions, while allowing for bends with low action in the high positions.
The best fretboard shape for good bending with low action is infinite radius: perfectly flat. If the fretboard is flat and the frets are straight lines, then bending a note doesn't bring the string any closer to any fret, and so there is no onset of buzz.
Thus, what might be "too low" on one guitar can work great on another.