I wonder how his supporters deal with the fact that, if his test wasn't falsified, then Djokovic's plan for getting into Australia was apparently to catch COVID almost exactly when he claims he did.

I.e., at some point Tennis Australia told Djokovic's team that he would/might get an exemption if he'd had COVID recently. In early December Djokovic hadn't had COVID recently and didn't qualify for any kind of exemption. It is very fortunate for him that he then caught COVID, and in time to recover before the event. In early December Djokovic must have been expecting to NOT compete in the Australian Open, right?