It strikes me that what happened was that, perhaps with the best intentions, BA offloaded him from the MIA flight because they believed he wouldn't make it. In fact, as the MIA flight was itself delayed, he made the connection quite comfortably.

Regardless of whether this was a foul up, or just BA making a judgement call which, in hindsight, proved erroneous strikes me as irrelevant. He presented himself for boarding in good time, and was denied.

The weather may have been the proximate reason why BA even thought of offloading him in the first place, but it is actually a red herring in this instance.