When the rule change was introduced back in the 2002-03 season the NFHS made it clear that a team could use either type of time-out.
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.
It was clarified in later years that a team could even take an excessive time-out and suffer the technical foul to keep a player in the game, if desired, as well as that if a player from each team was injured, then each team needed to take a TO to keep its player in (current NOTE to 3-3-6).
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