If they are required to do business with one another how do they negotiate a price?

Lots of companies that are required to do business with each other (eg. utilities and the rest of the private sector or large retailers and large consumer goods companies) are able to do it, why would a statutory requirement be any different?

How does it work in Maryland, where this is already the law?

Heavy regulations & requirements on the insurers.

You set the price based on what is reasonable and customary.

Like Medicare.

There are lots of doctors who don't accept Medicare patients because the reimbursement rates are too low.

Okay. So we write the check to IBM to improve/license Watson for all of Medicare to use. If doctor's won't accept the payments available, automate what we can, and provide more training to nurses to enable them to fill in.

Yes, I'm advocating for the replacement of doctors in the vast majority of cases. They're like college professors who spend most of their time doing research, while the TAs (Nurses in this case) do all the heavy lifting. Empower the nurses, replace the doctors.

Sorry, but Watson can't do surgery, nor can it instruct a nurse who has no training in surgery how to do surgery.

Yet.

http://www.intuitivesurgical.com/

... which is why there's laws like the aforementioned Maryland law that requires them to accept all insurance.

But that kind of policy will eventually backfire, since doctors are free to move to whatever state they want once they finish their residencies. If Maryland forces them to accept insurance that doesn't reimburse them at a rate that they find acceptable, they'll go work in another state and Maryland will have a shortage of doctors. And doctors who are already practicing in Maryland will retire early or move into research, or some other job that doesn't involve seeing patients (like consulting for medical software companies).

I'm guessing current laws were written around the "managed care" (HMO/PPO) system, the previous (70s-90s) attempt at healthcare reform.

For that one, the theory was that the payment/administration bureaucracy was the cause of the health care cost problem, and that by having insurance companies buy hospital service in bulk rather than doing individual-service billing the overhead could be reduced and accountability would be increased. This requires insurers to be able to assign customers to hospitals and doctors that work for them for it to work.

Johns Hopkins is a "chain" hospital?

No, but most hospitals are.