If A-1 is injured and Team A requests a time-out before a replacement, is the official's action correct?

In this scenario, the official's action of denying the time-out request is indeed correct. According to the rules of basketball, when a player is injured, the coach or team can request a time-out so that the player can be replaced, however, the official may not allow a time-out request to be granted if it comes in the midst of a situation where the game does not permit such a pause, such as when the official is in the process of administering a free throw or if the ball is in play under certain conditions.

When an injury occurs, the priority is to ensure the safety of the player, and the game must adhere to set procedures to maintain proper flow and integrity. The game only allows time-outs to be called under certain circumstances. Granting a time-out when it is not permissible would disrupt the game unnecessarily. The rules are clear on this aspect, prohibiting time-outs in certain contexts, especially concerning injury protocols, to keep the game’s rhythm and fairness intact.

Ensuring the game is played fairly can involve denying time-out requests in scenarios where such requests contravene established rules or game flow. The other choices imply conditions or situations that do not align with standard procedural guidelines, which uphold the integrity of the game.