(CBS News) The University of Pittsburgh Medical Center -- named one of the ten best hospitals in the nation by U.S. News -- cares for the sick and saves lives.

As a nonprofit organization, it also receives a tax break. But in recent months there have been questions raised as to whether the hospital acts more like a corporation, reaping big profits and driving up health care costs.

According to an audited financial statement, UPMC made $948 million in profits from 2011-2012. And while tax returns show it spends just two percent of its yearly budget on charity care, the hospital receives a state and federal tax break of about $200 million, according to city estimates. Pittsburgh Mayor Luke Ravenstahl is suing to revoke its nonprofit status. His city stands to gain $20 million a year.

"I think they're going to be hard pressed to prove how they're operating the same way as the Little Sisters of the Poor or the Catholic Church, true genuine nonprofits. UPMC? I'm afraid not," Ravenstahl told "CBS This Morning."

The mayor said he was also surprised to learn that UPMC's CEO, Jeffrey Romoff, makes almost $6 million a year. That makes him the highest paid CEO of any large nonprofit hospital in the U.S., according to a recent analysis by TIME. Romoff also has more than a dozen administrators that take in annual salaries of over $1 million, and according to the city, he has access to a private chef, chauffeur, and a jet, as well as one of the most expensive office spaces in Pittsburgh.

Professor Martin Gaynor of Carnegie Mellon has published papers on hospitals that enjoy nonprofit status but do not always function like charities.

"There's a lot of concern here in the community," Gaynor told "CBS This Morning."

"They've taken some actions that don't appear to be consistent with an organization whose mission is to benefit the community."

Some of UPMC's funds are directed at facility improvement, but Gaynor has concerns about even some of that spending. He likened the new, state-of-the-art pediatric center to a palace.

"It's a tremendous asset to the community," he said. "On the other hand...one has to ask whether it was so important to make it so beautiful, or whether some of those dollars could've been used to better purpose -- to offer lower prices to members of the community, to offer more charity care."

While nonprofits are required to serve the community, UPMC has closed hospitals in poorer neighborhoods and opened them in more affluent ones, claiming the hospitals they closed were underutilized.

Some of the concerns in Pittsburgh have been echoed across the country. America's hospitals have been growing. The bigger they get, the more power they have -- to set prices and force insurers to pay more. Patients foot the bill via higher premiums, copays, and deductibles. It's one factor behind the nation's increasing health care costs.

"At the end of the day, when hospitals charge higher prices, who pays for them?" Gaynor asked. "Dollar for dollar, the rest of us."

UPMC declined an interview request from "CBS This Morning" as part of this report. After the story aired, hospital spokesman Paul Wood claimed on the radio station KDKA that there is no chauffeur or private chef, and that the local tax break is actually $15 million. Their own website however, references an "executive kitchen," that serves thousands of guests every year.