But Rick Wallace, the hospital's CEO, said in a Thursday interview that those allegations are false.
"Why would we want to do that?" he said. "San Juan Health Partners depends on a healthy relationship with independent physicians. We do scrutinize contracts, but that's just prudent business practice. You've got to have checks and balances. If they're independent (physicians), we pay for the first two years of salary and overhead. It's what's known as our income guarantee."
San Juan Health Partners is a group of physicians affiliated with the hospital. It appears the rumors may have been generated by the scrutiny of at least two of those contracts.
Although individual councilmembers did not specify their concerns at the Tuesday evening meeting, Councilman Jason Sandel and Councilwoman Mary Fischer elaborated during phone interviews Wednesday afternoon.
"The only way that we can understand better is to begin to review their operations," Sandel said. "It should be an open and transparent operation. There are significant tax dollars that go into (the hospital). It is absolutely a publicly funded institution. These concerns can be alleviated with transparency and openness."
Fischer expanded on Sandel's concerns.
"Last year I brought the plight of the physicians to the council's attention," she said. "The playing field is not equal. We're fully aware that we have nothing to do with the operation of the hospital, but I like an environment where the doctors make a commitment to their community."
Fischer said that some doctors are now leaving the community.
"I think we have a problem on our hands as a community," she said. "I think we do have a say in what goes on, albeit a second-hand say."
The full council agreed to direct City Manager Rob Mayes to request the last two years of the hospital's board of directors' meeting minutes.
"I wouldn't say there's a conspiracy," said Dr. Harold McFarling, a doctor of osteopathic medicine in private practice who sees patients at the medical center, in a phone interview on Thursday.
"I've heard of some individual practices that could have been handled differently, but I don't know the specifics," McFarling said. "Unfortunately, we've seen some situations where contracts with individual physicians have not been renewed."
McFarling served on the hospital's board of directors for four years, from 1998 to 1999, and from 2006 to 2007. He was the hospital's chief of staff in 1999 and 2007, and was the vice chief of staff in 1998 and 2006.
He added that his comments are his personal observations.
San Juan Regional Medical Center has been working to provide attractive opportunities for physicians to serve the community, Wallace said.
"There are two models that individual physicians choose to practice in: employed and independent," he said. "The employed model is becoming more of a preference. Younger physicians are seeing the writing on the wall."
Wallace said, increasingly, young physicians across the country are choosing to work for hospitals, which provides a more secure work environment.
One of the hospital's independent physicians, Dr. Allen McCulloch, a urologist, is hoping to bring another urologist, who would be able to see patients at the hospital, into his practice, Wallace said. In addition, the hospital is looking to fill three other positions with independent doctors.
The hospital is currently searching for ten doctors in different specialties, according to information Wallace provided the Daily Times.
"Today's world of physician recruitment is not as simple as it was five years ago," Wallace said.
But patient care is the priority, he said.
"(Hospital) administration and our board of directors, we are going to make sure the access needs are being met," Wallace said. "I think there is an opportunity to start looking for new physicians."
The hospital's level-three trauma center designation is also secure, he said.
"We have all the specialties," Wallace said. "That will never be in jeopardy. (The center) never depends on one specialty. It's a group effort."
And the scrutiny of contracts for physicians with San Juan Health Partners is part of an annual process, he said.
Wallace said that there is a physician providing nursing home services, and that individual's contract was being reviewed, as well as a neurosurgeon's contract.
"It's a mutual decision on contracts," he said. "Nobody's contract is not being renewed. It's our business to keep them in a sustainable practice."
Greg Yee can be reached at email@example.com; 505-564-4606. Follow him on Twitter @GYeeDT.