When emergency medicine emerged as a specialty in the 1980s, almost all E.R. doctors were hospital employees who typically did not bill separately for their services. Today, 65 percent of hospitals contract out that function. And some emergency medicine staffing groups — many serve a large number of hospitals, either nationally or locally — opt out of all insurance plans.

As more insurance plans contract with narrower networks of doctors to form offerings tailored to the Affordable Care Act, insurers have acquired greater leverage in cutting payments to physicians. While an insurer would have little power to drive a hard bargain with a major hospital that the company needs in its network, it can often pick and choose among physicians, excluding some or offering rates so low that many doctors say their practices are unsustainable.

Dr. Jeffrey Bettinger, chairman of the reimbursement committee of the American College of Emergency Physicians, said that out-of-network emergency room doctors were an unusual phenomenon and expressed doubt that the practice was widespread. When it occurred, he added, it was typically because of insurers’ unwillingness to pay doctors a reasonable rate compared to what they pay hospitals for their services.

The average salary of an emergency room physician was $311,000 in 2014, rising from $247,000 since 2010 — a period when many other types of doctors experienced declines in salaries, according to Merritt Hawkins, a physician staffing firm.

Hospital charges for emergency care vary widely. A recent study found that hospital charges for a visit involving a serious medical issue in California varied between $275 and $6,662, just for the facility fee. “Much of the variation we observe may in fact be entirely random,” wrote the authors, emergency physicians at the University of California San Francisco Medical Center. But that variation often does not directly affect patients, since most hospitals participate in the big insurance plans in their area, and patients tend to know which are in their network, so the insurer covers most of the bill.

But it is a different matter with emergency room doctors who bill out-of-network fees, experts say.

When Dr. Michael Schwartz’s daughter went to an emergency room in the Philadelphia suburbs for a reaction to a medication in 2010, she went to an in-network hospital, Bryn Mawr. She was there for a few hours on a cardiac monitor. While most of her care was covered by his family’s insurer, Capital Blue Cross, a bill of more than $2,000 from the out-of-network E.R. physicians for cardiac monitoring was not.