But a mathematician could give you an accurate probability that you would survive the procedure carried out by that surgeon
Sorry, I know that's pedantic!
The thing is that a problem as vast as climate change needs a multidisciplinary approach. You need oceanographers to measure the ocean currents, climatologists to study past and current climate, astrophysicists to assess the effects of the sun, geologists to assess the prehistoric data, economists to assess the costs of action vs inaction, mathematicians and statisticians to actually create a model and provide as good an answer as they can, as well as biologists, chemists etc to monitor secondary effects on species numbers, ocean acidification and so on. All of them are needed to both carry out the primary work and evaluate it (mathematicians and statisticians would be vital in this as they would assess the methods used to interpret the original data, which you could argue is the most important step anyway).
On the other point you make, I would also not sign a document that I agreed to something I'd never seen, so fair enough, and if that's true I agree it's a pretty poor state of affairs for such an important topic. On the other hand, I'm deeply suspicious of statments that begin with 'apparently'
