This a house rule that was never strictly enforced upon our gaming group, but one I personally enforce upon MYSELF:
If a hero has a modifier/reroll in the exploration phase, I roll a different colored dice for that hero. For example, I have three heroes with lucky rabbit's feet, and two without. It would make perfect sense, considering that a hero cannot reroll another hero's attack roll, that he cannot reroll another's exploration roll. Thus, I have three dice that I can reroll, if I so choice, and two dice that I can roll only once (and get stuck with the result.)
Again, this is not 'the letter of the law', but it makes sense for the sake of fairness and flavor.