The only way to stop this from happening is blocking the model's release at the first place. Which requires China agreeing to the same framework. Dario says exactly the same thing himself.
So if he's being truthful here, he's not advocating for the type of ban people are talking about (usage ban). This kind of ban would be helpful to Anthropic's business in the short term, but it won't prevent Chinese models from improving, and it won't prevent them from getting money selling to other countries.
He is openly advocating for an international effort to enforce tests on public models, but I think this is highly unlikely in the current climate. Even if both the US and China agree that public models should be prevented from being used in designing bioweapons, they need to agree on a test and enforcement framework and that requires a lot of negotiation and trust. I don't see this as likely in the near future.