I don’t think guys are exaggerating how far they are hitting it. I think they just suck at judging distances. This thread has answered a lot of questions about the distance of shots on deer.
I can't speak for other guys but but when I play I use a scorecard app instead of pencil and paper scorecard, and it uses GPS to measure distances, so I'm pretty confident my yardage are dead on. I've compared the yardage on the app against scorecards, sprinkler heads, fairway yardage markers, etc...and its usually within a couple of yds.