This is exactly the thing. Your mathematics may be absolutely watertight, but if your starting assumptions aren't based in reality then your result isn't going to be either. Garbage in, garbage out – and that's going to be true regardless of how "hard" or "soft" your subject is.

You could derive perfectly sound results about the population dynamics of pigs assuming that they can fly, but biologists are going to tell you you're wrong regardless of the maths – and rightly so.