Watching umpires and referees make game-deciding calls on inherently ambiguous plays has accustomed people to the idea of what scholars call underdetermination. That is, sometimes the facts are insufficient to decide between competing views. Nonetheless, a decision is a decision. The public was committed to the whole process, and not just the part on Election Day. Philosophers have argued for ages over the paradox of foundationalism.
Truths can justify each other.
In 2000, the public rejected political foundationalism. It rejected the notion that legitimacy springs from an incontestable election result. There was no incontestable result, nor was one necessary. Political decisions can justify each other. The Founders hoped to create a political system that was better than politicians.