Why is this such a big deal- if you don’t want to use an organization because you like a different one better, or for any personal reason, then in case of need reach out to the one you are more comfortable with. Besides, why would Hatzalah mind if others step up to the plate, if their goal is to save lives. Hatzalah has B”H successfully served the various Jewish communities for decades. If/when another group proves their level of professionalism to YOU, and you would prefer, call them.