Apparently that's not 100% true. The DoD contractor itself can still use Anthropic's technology, just not on U.S. military contract projects.
They will stop just to be sure no boundaries are crossed.
The issue is the onus is on the contractor to prove that Anthropic technology has not tainted US government contracted projects - this is a herculean task verging on impossible. Additionally, most contracts will mandate SLAs around removing BOM risks.
If you were a contractor to DoD (no way I'm calling them DoW) would you take the risk of doing business with a company that has been labeled a supply chain risk by your main customer?