WOW! This is a shocking answer!! Nothing in the rules would really indicate that lots of units could try reactive fire in a single turn, to the contrary, the rules would seem to indicate only ONE can do it.
It's a pity that Zach messed up his previous answer on Reactive Fire against Fast units, because now I'm not fully trusting this answer. I mean, this could be the rules, but the rulebook really doesn't point us in that direction.