The solution, of course, lies in the Many Worlds interpretation of quantum mechanics. As we all know, if a waveform can collapse into one of two states (Schroedinger's cat is either dead, or alive), then in the Many Worlds version it does both. This Universe bifurcates into one where option A occured, and another where it was option B.
Now it turns out that Santa is Omniversal: he exists simultaneously in all Universes. His actions in any one Universe are translated to all similar Universes. In this way he is required, in each individual Universe, to deliver presents to only a single household, having ample time to eat the cookies, feed and water the reindeer, and tick off the list.
The only debunking that occurs to Santa Claus is when he gets out of bed.