The side who does not have the initiative is reacting to the initiative players current activate unit.
By using the reacting process to suddenly become the player with the initiative and activating a unit not involved is corrupting the rules procedure.
The writers (I'm guessing only) used the word reacting to instruct the player that he is reacting to a specific action of the initiative player. Otherwise you may as well have a IGOUGO play sequence where anything goes on your move.
That said, you paid for the rulebook if you want to rules lawyer them to death because the rule wording doesn't explicitly say you can't do something. That's your prerogative.
