These columns have been supportive of Governor Spitzer in his battle with Local 1199 of the Service Employees International Union and the Greater New York Hospital Association, two interest groups that have overreacted to Mr. Spitzer’s plans to slow by a modest amount the rate of growth in New York’s Medicaid budget. The battle grew more heated this week with the release of a letter by Mr. Spitzer to hundreds of hospital trustees arguing that “New York’s health care system is broken” and that “New Yorkers pay far too much and get far too little in return” for health care. The Greater New York Hospital Association responded by accusing Mr. Spitzer of threatening “our ability to provide quality health care to all New Yorkers.”

Mr. Spitzer has the better of this fight, particularly when he emphasizes, as he did in this week’s letter, that New York has the highest state and local tax burden in the nation, largely because of its Medicaid and hospital spending, which is twice the national average. But we don’t mind saying as well that there is a back-story to this feud that deserves at least a mention. It struck us the other day during a visit to the Greenberg Pavilion of the Cornell-Weill Medical Center on Manhattan’s East Side. One might make a similar observation after having visited the Komansky Center for Children’s Health at the Morgan Stanley Children’s Hospital of NewYork-Presbyterian, which is uptown.

The Greenberg pavilion is named after Maurice “Hank” Greenberg, whom Mr. Spitzer forced out of the chairmanship of American International Group, the insurance company that Mr. Greenberg devoted his life to building. Mr. Spitzer also forced Maurice Greenberg’s son, Jeffrey Greenberg, out of his job as chairman of Marsh & McLennan. Both Greenbergs are trustees of NewYork-Presbyterian Hospital, and one can only imagine their response upon receiving a letter from Mr. Spitzer in which the governor asks them to “join me as a partner.”

Another trustee of NewYork-Presbyterian — and thus a person Mr. Spitzer seeks as “partner” — is Sanford Weill. It is he and his wife, Joan, that the Cornell Medical School is named after. Mr. Weill had his own clashes with Mr. Spitzer after the attorney general unearthed e-mails in which a Salomon Smith Barney analyst, Jack Grubman, asked Mr. Weill to help get his child into the 92nd Street Y preschool and also discussed upgrading his rating of ATT stock. Citigroup, of which Mr. Weill was chairman at the time, owned Salomon Smith Barney and wanted investment banking business from ATT.

The Komansky Center for Children’s Health is named in part after another NewYork-Presbyterian trustee, David Komansky, a former Merrill Lynch chief executive who also has a history with Mr. Spitzer. A 2002 article in TheStreet.com reported, “After initially claiming that Spitzer’s allegations were ‘just plain wrong,’ Merrill Chief Executive David Komansky recently apologized for emails that showed analysts privately disparaging companies while publicly recommending them.” As for the Morgan Stanley Children’s Hospital, Morgan Stanley, too, was caught up in Mr. Spitzer’s probe of conflicts of interest on Wall Street.

At New York University Medical Center, the chairman of the board is Kenneth Langone, who was sued by Attorney General Spitzer for his role in setting the pay of Richard Grasso when Mr. Grasso was chief of the New York Stock Exchange. Mr. Langone later emerged as a big backer of Mr. Spitzer’s opponent in the Democratic primary for governor, Thomas Suozzi. We are not questioning any motives on the part of anyone here, including Mr. Spitzer. No doubt many — or, more likely, most — of the hospital trustees have never been in activities that landed them on the business end of a lawsuit or an investigation by Attorney General Spitzer.

We don’t suggest it’s anything but coincidence that the hospital fight pits the new governor and at least some figures he confronted when he was attorney general. But if Mr. Spitzer is serious, in his letter, about inviting the hospital trustees to join him as partners, maybe he should start by ringing up the Greenbergs, Mr. Weill, Mr. Komansky, Mr. Langone, and Mr. Weill, and asking them personally. It could be the beginning of an interesting conversation.