I would not agree with you, and I think you can't compare programming and math in this regard. The "beliefs" they are talking about are rather trivial: strictly formal abstract logical statements which look very hard from intuitive point of view, but they are relatively easy to construct and relatively easy to disprove (provide a counterexample for). An attempt to base your work on one would instantly lead to an error in a proof, which will be found upon review.

On the other hand, programming is actually a branch of engineering, a much less formal discipline. TIMTOWTDI, and not just in Perl. Everything in programming is subjective. Results of programmer's work aren't simply "correct" or "erroneous". Basing your work on a "false belief" will just require spending more effort on it, or lead to a lower quality product.

You can imagine an objective false belief, but it would be some kind of triviality, like wrong understanding of initialization order for base classes in C++, or behavior of modulus operator for negative numbers. Nobody is discussing this kind of stuff with any grandeur.

edit: tl;dr: in math it may be hard to understand whether you're objectively wrong. In programming it is usually as trivial as a compile-time or runtime error, so programmers will usually discuss subjective issues.