Hare's theory predicts that there would need to be a cold snap at just the right time, and lo and behold there was. Probability isn't an issue if the only reason you are considering the probability is because the event already happened. Indeed the low probability of such an event transpiring goes a long way towards explaining why the discovery was not made earlier.

Root-Bernstein's theory makes no such testable predictions, and it solves the issue of an incomplete record on September 3rd with incomplete or inaccurate records elsewhere. It seems to me extremely plausible that fleming did not record the results of a botched, uncontrolled experiment but still recognized it as an indicator of something interesting that warranted follow-up. If I were in his position I would preserve the random dish for comparison to the more rigorous follow up experiment. I certainly don't put any stock into the argument that if the story had gone as Root-Bernstein describes it would have been too circuitous for scientific publishing, if anything it would be much more harmonious with standard scientific writing than the chance observation story.