No, in your example, if the dodgy Chinese company is a supply chain risk due to sabotage, why would they invoke an act to force production of the bolts from the same company for use for national defense preparedness, which would be clearly a national security risk?

The OP specifically mentions this in the context of "systems" (a vague, poorly-defined term) and "classified networks" in which Anthropic products are already present. Without more details on what "systems" these are or the terms of the contracts under which these were produced it's difficult to make a definitive judgement, but broadly speaking it's not a good thing if the government is relying on a product which Anthropic has designed to arbitrarily refuse orders by its own judgement.

I really don't see how anybody could think a private defense contractor should be entitled to countermand the military by leveraging the control it has over products it has already sold. Maybe the terms of their contract entitled them to some discretion over what orders the product will carry out, but there's no such claim in the OP.