If you listen to the government officials explain the situation:
All this began after the Maduro raid, when executives from Anthropic allegedly called an intermediary vendor, Palantir, seeking specifics of how their software was used. Because this is classified information, Palantir refused to disclose it, which led to Anthropic threatening to shut off service to Palantir. Palantir reported this to the pentagon who then contacted Anthropic directly.
Obviously, the military can’t have Palantir’s services suddenly stop working mid-operation because one of their suppliers objects to it. So they can’t risk having Claude anywhere in the supply chain.
Assuming the government isn't lying, then the designation is completely and entirely appropriate. You can substitute out any other vendor, and they'd receive the same treatment.