Claims of US election fraud: fallacious assumptions of statistical independence

Assuming statistical independence for events that are anything but independent is a staple diet of election-time fake news. The best example is this claim — made in court — that I reproduce in its full glory:

The ‘argument’ is this: assume each vote has a fixed probability of going to Biden or Trump. What is the chance of Trump being as far ahead as he was in Georgia, Michigan, Pennsylvania and Wisconsin at some point in the count and still going on to lose? Unsurprisingly, under the assumption made these are pretty small. Since the final Biden vote share in those states is around 50%, they would equal the probability of tossing a fair coin hundreds of thousands of times and have it land heads significantly more often than tails.

However, the ‘coin’ analogy — and the whole claim — assumes statistical independence, it assumes that every vote is equally likely to go to Trump or Biden. This is clearly, manifestly not the case because it is known that mail-in votes — which take longer to count — were added to the totals towards the end in those states. (In states like Florida and Ohio where most of the mail-in votes were counted before the election Biden went out in front in the early stages of the count but was caught and overtaken). In addition, metropolitan areas — Democrat strongholds in this election — were usually counted near the end. Each vote is therefore not independent, which invalidates the whole approach.