I agree. Get the sub in. The 45 second limit for subs is for normal substitutions. For the blood rule/timeout the player is allowed in at the end of the timeout if they are ready. If not, direct that they be replaced as we have always done. A sub is never required to be ready ahead of time when a player has been directed to be replaced. The timeout does not complicate any of this.
There are rules/cases that exhibit replacing players at time where subs would not normally be allowed. For example, a player has committed 5 fouls. 2 FTs are to be shot. Player is replaced immediately, while any substitution situation without a DQ would have to wait.
A player that is required to leave the game can be replaced without limit (except that the substitute must have been out of the game long enought for the clock to have been run).
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