15 cents is huge. It's 15% of the way to the next note. Even 5 cents sounds noticeably out of tune. Trained musicians can easily tune to less than 2 cents without using tricks like beating to get even more accurate tuning.
Guitarists may be out of tune, but chances are more likely you're hearing a poorly intonated guitar. You can tune the open strings perfectly, but if your string scale-length deviates from what your fretboard expects, you'll have notes that progressively get more out of tune the further down the neck you play. You can't correct this with tuning, you need to adjust the tensions in your bridge saddles, and most amateur guitarists are afraid to do this.
Also you mention live settings, it depends on how big the group is I guess, but at smaller venues and smaller bands the stage monitoring is often so bad you can't hear your own guitar.
Guitars being out of tune happens because of the frets, not some lack thereof; most people tune each string with a tuner and/or by comparing to other strings, which means that some notes will be in tune and others will be very out of tune. This is one of many possible motivations (arguably the primary one besides ease of fingering) for tunings other than the "standard" EADGBE tuning: to change which subset of possible chords are in tune.
This is arguably a non-issue for fretless guitars, but those take more skill to play (and I'd imagine getting some chords perfectly in tune would entail nigh-impossible hand contortions even without there being frets involved).
Any proof to this? 12 tet can vary by 15 cents from just intonation. Even an amateur musician can hear how out-of-tune a 15 cent difference is.