Do you make this argument in any other scenario? I'm sure all merchants who accept credit cards combined make WAY more than Visa/MC, but I think most would agree Visa has much more leverage over a corner shop that accepts Visa than the other way around.
There are 5 or 6 big insurance companies, maybe 2000 if we count all of the small ones and 400K medical practices. So even by this very simple money=leverage argument, each individual practice has far less money than the insurance company they are dealing with. So if more money = more leverage then these same numbers prove the opposite claim.
So its probably fair to say that the picture isn't as simple as money=leverage.
If a medical practice and an insurance company get into a dispute and one of them decides to not work together, the practice loses say 1/5th-1/10th of its customers, the insurance company loses 1/100000th of its revenue. I call that leverage.