Here you go...
From the 2002-03 NFHS Rules Book on page 70 and also appearing on page 3 of the 2002-03 NFHS Case Book:
Comments on the 2002-03 Rules Revisions
Player with blood or injury may remain in game with a time-out (3-3-5 & 6): This change permits a player who is required to leave the game for blood or injury to remain in the game if the team calls a time-out (60 or 30-second) and the situation can be corrected by the end of the time-out.
Teams may use successive time-outs to correct the situation if permitted by rule and if adequate time-outs remain. The previous rule had a potentially tremendous impact on the game when a player had blood on the uniform or body (which may not even have been their own) and was required to leave late in the game, without the ability to immediately return. Under this new rule, if a team desires to utilize a time-out and can rectify the situation by the time the ball will be put back in play, the affected player may remain in the game.
*I also found an NFHS interpretation from that same season which states that a team may take an excessive time-out if it so desires in order to keep an injured or bleeding player in the game.
2002-03 NFHS BASKETBALL RULES INTERPRETATIONS
Publisher’s Note:
The National Federation of State High School Associations is the only source of official high school interpretations. They do not set aside nor modify any rule. They are made and published by the NFHS in response to situations presented.
Robert F. Kanaby, Publisher, NFHS Publications © 2002
SITUATION 6: In the last 30 seconds of a game, a player from each team has blood on the uniform. Team A has a time-out remaining and Team B does not. RULING: If the officials direct both players to leave the game, both teams must call a time-out to keep the respective players in the game. The player for Team B must leave the game since his/her team is out of time-outs.
COMMENT: Team B could call an excessive time-out resulting in a technical foul to keep the player in the game. (3-3-6)