From a scouting perspective, I think a lot of people tend to focus on the wrong things.
Is 7/19 impressive? Not overly but the one minute stretch, with 5 minutes left, where Barnes single handedly got them over the hump (and gave them a chance to win) indicates he has that top gear. He just needs to figure out how to get to it a little more often.
He had a steal, a three, a rebound, layup (and 1) and jumper (and 1 missed). In a minute, he scored 8 points and finally broke through the 2 possession barrier UK had held for almost the entire second half.
While UNC eventually lost and Barnes missed some shots down the stretch, the ability to have a one minute burst is certainly something you should not ignore. Scouts measure heavily on pro potential, they don't measure strictly on college production and certainly not on a game to game basis.
In his last 15 games, Barnes averaged 19.1 points, 6.3 rebounds and shot 44% from the floor. While the 44% from the floor is a bit lower than you'd like, it's not alarmingly low (especially if you get him to shave a few threes off his shot selection). It also crept up a bit from the 40.7% in the first half of the season, which certainly isn't a negative.
Do I think Barnes is a perfect prospect? Well, no but people just seem to flat out ignore his performance over the second half of the year. Given his prototypical size (6'8'', 210 lbs), I would have to roll the dice on him over many of the other players who might be more of a finished product at this point. Stars win in the NBA. Rotational players don't. When in doubt, you always gamble on the star (or the guy who could become a star) IMO.
There's clearly some questions the FO would need to answer (or at least be comfortable with) but I don't think there's the one huge red flag that just can't be ignored. Some people question his athleticism but he certainly didn't look pedestrian against a very athletic UK front line. I'm sure his individual workouts will clear up much of the debate on his measurables.