It is a question that has plagued lawmakers and medical experts for nearly a century. As early as 1910, Abraham Flexner wrote a landmark report that argued teaching hospitals should be staffed only with salaried doctors. In 1970, the Carnegie Commission released a report calling for drastic improvements in rural health care, and highlighted Bassett as a model.

Many doctors who work at Bassett believe deeply in its mission. Bassett has opened 13 clinics in schools around the region. The clinics lose money, but Bassett is considering opening 14 more.

“I was in private practice for years in New Mexico,” said Dr. Philip A. Heavner, the chief of pediatrics at Bassett, “and there was no interest in doing anything like this because people thought it would take volume away from their practices.”

Dr. Randall Zuckerman, an attending surgeon at the Hospital of St. Raphael in New Haven, left Bassett a year ago because his wife wanted their four children to grow up closer to family. Since many of his patients see fee-dependent doctors, Dr. Zuckerman said in an interview, their care is more disjointed than was common at Bassett.

“They get a lot of different consultations, some necessary and some not,” he said. “They are always missing parts of their medical records because the information is coming from multiple private offices.”

Michelle Griffiths, 41, of Edmeston found a lump on her breast six years ago. During cancer care at Bassett, Ms. Griffiths’s appointments to see her oncologist and primary care doctor are often scheduled on the same day. One doctor will sometimes accompany her during a procedure performed by another, and each has her complete medical history.

“The communication amongst all of my doctors is impressive,” said Ms. Griffiths, who works as a database administrator for the insurance company New York Central Mutual. “They always call each other or shoot each other e-mails.”