The one put into play by the PU is not the ball in play. If any play is made using that ball, I would definitely be trying to figure out how fast I could kick the PU in the a$$ for that stupid action. I believe "Time" would have to be called and place the runner(s) where the umpires thought they would end up. But, if F1 gives the ball back and nothing is done with that ball and no one plays off that ball, then don't reference the screw up. But, I would still be looking to put my foot up the PU's a$$.
That is just how I would handle it. Probably lose my job afterward and be down 2 umpires. PU with my foot lodged in his a$$.