This discussion has nothing to do with the rules, but rather whether or not we are going to decide to intentionally set aside a rule (which is very clear in this particular case).
I refer you to the NF Case Book:
7.5.2B. Play: Team A is awarded a throw-in near the division line. The administering official by mistake, puts the ball at B1's disposel. B1 completes the throw-in and Team B subsequently scores a goal. Ruling: No correction can be made for the mistake by the official.
So, what are you going to do? Go against what is clearly in the rule book?? As officials, we don't have the authorization to set aside a rule just because we don't like it, or the outcome of it.
If you screw this up, it is your fault and there is nothing that you can do about it. Setting aside the rule will only make matters worse.
Think about the last time you saw an NCAA Division I game where one official signaled a charge and the other a block. What did they do? They went to a double foul call. Why? Because that is the
rule. Setting aside that rule in an attempt to avoid some embarassment will compound the problem.
The heart of the issue is fairness, and if some officials choose to set aside certain rules simply to save face, or for any reason at all, the game is not being played fairly at all.