Hinch, who was dismissed a week later along with general manager Josh Byrnes, had to make a difficult decision in that game.
While Jackson did have a no-hitter going, he also walked eight, so his pitch count was very high. In fact, he finished with a whopping 149 pitches.
Jackson's name was brought up to Gibson, because the right-hander, who is now with the Nationals, started against Arizona on Wednesday night.
"You know what I remember about that game?" Gibson said. "When A.J. asked me in the seventh inning, what should I do? I said, 'I'd take him out.' I would have never let him go that far. It's dangerous. If I were the manager at the time, I would have pulled him."
The outing did not seem to damage Jackson's arm, as he has stayed healthy since.
True, he did have a 7.24 ERA in the month of July, but he had his share of struggles before that as well, and he compiled a 1.47 ERA in August.
"Edwin is, in all honesty, he is a very unique athlete," Gibson said. "He's elite. He did OK after it, but it did have an effect on him. You're thinking about one game here. I would assume it would have a negative effect on the future, at some point. The thing you would worry about is if he blew his shoulder out or something like that."
Gibson said he would not allow a young pitcher like Wade Miley to throw 130 pitches in pursuit of a no-hitter, but might allow a veteran like Ian Kennedy or Joe Saunders to do so.