Injury rule quesion?

[LIIRISHMAN]

I had a 16u girls FP game with something I have not had to address yet as a umpire.There was a trainwreck in the 6th inning at 1st base between the BR and 1st baseman,BR was ruled safe.The BR was crying and was shaken up and was taking back to the dugout.There was a delay of several minutes while they tended to the player.The Coach informs me he had no subs and I told him that he would have to take a out.(he's up 8 runs at this point).I informed the Official scorer of the out and I'm ready to start play when the injured player tells the coach she wants to go back in to play. Coach asks me and I let her go back to 1st base. Now the coach of the defense is out to argue that the girl was declared out and should be ineligible.My reading of the injury rule is that she can come back at any time. Since no pitch was thrown I rescined the out and let her go to 1st base.Was I right? Also if play had resumed and a play had occured could that player re-enter and the out be rescinded. I looked through the book without finding if this would be allowed.