Let me explain how it looks from the viewpoint of the manufacturer. Very different rubber compounds are used for different models of bicycle tyres. A wired tyre made of hard rubber has its sidewalls prone to crack more easily than a foldable tyre made of soft rubber compound. Hence, the higher minimum inflation pressure for the former. In the case of the conflict, one must conform to the manufacturers safety limits. If the calculator reads 51 psi for Firm and the minimum is 50 psi, the rider has to choose 50-51 psi and no adverse effects would happen.
It has nothing to do with snake bite puncture, only the sidewall durability. General rule (found in other sources such as Silca) is the rider shall start experimenting at the minimum allowable pressure for given tyre. By the way, what is the model and size of your tyres
@BEC111?