Not really. PADI does not pay the instructor. If the instructor is working for a dive shop, the shop sets the conditions of employment and provides the pay. If the instructor is an independent, then the instructor sets the conditions, receives the pay, etc. They may purchase classroom materials from PADI, but the fact that they purchased the dive gear from a someone like Mares does not make them agents of Mares, does it?
Doctors and lawyers graduate from school, get licensed from the states in which they work, and pay annual dues to the AMA or ABA respectively. They are not considered agents of their schools, the state, or the association to which they belong. If they commit malpractice, they can lose their licenses. If they commit malpractice, though, no one sues the college from which they graduated, the state that gave them their licenses, or the association of which they are members.