I looked at the tuner again, the G doesn't really hit 0 cents but right at the end of it, it gets close, then he pops up to C. The majority of the duration of that note, it's 30 cents low. Right at the end it goes up, hard to say if that's just part of the transition to the higher note. So I'm not sure if it's a version of F#-G-C or not.
Maybe it's a sort of "blue note" in the original meaning of that term, which means a microtonal note, not a flatted note.
The general theory is that blue notes (which aren't only present in African-American music; old time fiddlers also do this as a result of fingering methods) represent an attempt to avoid the half steps inherent in diatonic scales. Unfortunately the C major scale or C7 scale have whole steps F-G-A, so I'm not sure how the theory applies to the common use of a blued fifth.