Should a judge fix a solution agreed to by players?
Players cannot make rulings, that should be obvious; only judges can. 

From the Tournament Rules:


  Judges do not intervene in a game to prevent illegal actions, but do intervene as soon as a rule has been broken or to prevent a situation from escalating. More information on floor judge responsibilities can be found in the Magic Infraction Procedure Guide.


So if a rule has been broken but the game has continued, whether or not the players are aware that a rule has been broken, the judge will intervene as soon as he or she is aware of the situation.

Players can only make decisions regarding how to play the game, and if it comes to the attention of a judge that game rules have been broken, the judge will try to restore the game to a correct state as best as possible up to and including restarting the game, and/or will issue the necessary penalties according to the Judging at Regular REL rules or the Infraction Procedure Guide after evaluating all the evidence and assessing the situation.