This is mostly a zero sum game in the immediate term, and mostly zero sum in the longer term since there is a fairly limited pool of people available to fight fires. If you have the skills to be a fireman but a private individual pays you above market rate to fight their own personal fires then you will remove yourself from the pool of people fighting fires for the public and into a private pool.

Will 20 such private firemen be a problem? No, but 2,000? That would absolutely have an impact on available firefighters for the public.