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.
There's nothing stopping you doing this, you may feel that this will make your opponent break off his current attack to deal with the new threat. But as I said, you'll find yourself concentrating all your efforts where the action is. We had units left at the back of the table because we couldn't spare command tokens to move them forward! 
These units acted like a reserve, once our forward troops had weakened the enemy and taken a battering themselves, we pulled them back and advanced our fresh troops to finish off the job. Worked brilliantly and played superbly. The best, most fun WWII game I've played in ages. I've found that a lot of the problems brought up on this forum don't seem to be an issue when you're playing the game, if they are to you, then a simple house rule usually fixes it.