They claim two things:
1) The specific, available jailbreak for Fable 5 is not dangerous - this has been confirmed by multiple experts, and there is no credible evidence against this claim (in other words, Anthropic is probably correct)
2) It is impossible to build an LLM that is immune to all jailbreaks. Again, there is no credible evidence against this claim, i.e. Anthropic is again entirely correct.
If #1 was false, they could just publish the details of the jailbreak - it supposedly only works on Fable 5, so there's no possible danger.
If #2 was false, surely some other LLM lab would have done it by now. Especially since a number of governments have made it clear there is a market for such a project.