"We think it's responsible for us to remind the people involved that we believe we own the use of the Harvard name and how it relates to teaching and research and medical education," Wrinn said in an earlier interview.
Harvard Pilgrim has 1.1 million members, including more than 5,000 Harvard employees and their dependents, Fineberg noted in his letter.
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Erica B. Levy and Joyce K. McIntyre contributed to the reporting of this story.