The surgeon went to social media blaming UHC for everything, with the assumption that her own staff couldn't have been part of the miscommunication or paperwork errors.
UHC comes back, with receipts, showing that the error is somewhere on the hospital side.
UHC is still legally deficient in that hypothetical. Defamation of a public figure needs actual malice and knowledge (or reckless indifference) of falsehood—both absent.
There's a large gulf between being wrong and being libelous.
That's not actual malice. The doctor has no positive obligation to spend time reading UHC's letters pleading their version of the story, or interact with them in any way at all. Failure to engage with them is not malice.
The surgeon went to social media blaming UHC for everything, with the assumption that her own staff couldn't have been part of the miscommunication or paperwork errors.
UHC comes back, with receipts, showing that the error is somewhere on the hospital side.