Even though the odds of there being a secret conspiracy or master chess player behind the result are very low, that just seems better than the odds of chance getting the result. Most conspiracy theories rely on this sort of logic. The official explanations seem so unlikely that they must be part of some conspiracy to shield the truth from the public.

A good example of this is the last election. No sitting president has seen a double digit increase in his vote, but still lose. In fact, no one has been able to find an example like this in other elected offices. That's how rare it is. This once in forever thing could be accepted in isolation, but it is just one of such things. There are so many unexplained anomalies that people are naturally skeptical. The invisible hand of design, even without hard proof, seems like the more likely explanation.