The difference between your example and the Weather/Climate example is that coin tosses are based on a mathematically random premise, climate change assumptions

The difference between your example and the Weather/Climate example is that coin tosses are based on a mathematically random premise, climate change assumptions are based on giant, complex models with a large number of subjective inputs, many of which can trigger significant or subtle changes in outputs. A climate model is not proof and can not (yet?) be reasoned about mathematically.