player with blood

[sc/nc ref]

I need help on a situation that happened in a game tonight. Player was at FT line to shoot 2 free throws. Before the first ft, one of my partners noticed that the shooter's knee was bleeding. The Coach was told that he could call a time out to fix the problem or he could replace the shooter. He decided to replace the shooter with a substitute. After the substitute player shot the first free throw, the bleeding player (now with band-aid) was back at the table ready to check-in.
I determined that since a time-out had not been used to "buy" the bleeding player back into the game that the player would not be eligible to re-enter the game (and thus was not eligible to shoot the second free throw) until time had run off of the clock.
Was this administered correctly?
Thanks!