One nuance I've noticed: the statement from Anthropic specifically stated the use of their products for these purposes was not included in the contract with DoD but it stops short of saying it was prohibited by the contract.

Maybe it's just a weak choice of words in anthropic's statement, but the way I read it I get the impression that anthropic is assuming they retain discretion over how their products are used for any purposes not outlined in the contract, while the DoD sees it more along the lines of a traditional sale in which the seller relinquishes all rights to the product by default, and has to enumerate any rights over the product they will retain in the contract.