5. The players do not cheat.
To put the problem another way, all players of the team are housed in separate rooms. Everyone is informed about the colour of all others' caps by an arbiter. There is absolutely no possibility of learning more information than those colours.
Mirror in the room, not cheating; just not handled by the rules.
Arbiter gives away the cap's color, not a team member; so again, not handled by the rules.
The statement "There is absolutely no possibility of learning more information than those colours," makes the game impossible to win without wild guessing; so, either the statement is false and one can deduce the color of his/her own cap or it is true and there is no point in trying to figure out the game as it is always a 1/3 chance of winning (possibilities are correct, incorrect, abstain).