Hm...I think the reality is such that if the person doesn't have a degree in CS or Mathematics, chances of her being shortlisted for an interview aren't going to be high.
What might happen, though, is that the person develops considerable experience and expertise in programming whilst holding a job that isn't about programming. For example, the person could be doing some research work but makes use of programming to solve the problems at hand. Provided she has become competent in programming as a by-product, she can then market herself as a Programmer even though she doesn't have the background in CS or Mathematics.