As horrible as the DMCA is, it does not mean that Mozilla or any other hoster has to honor any claim anyone thinks up. If they are confident that a claim is frivolous they can just tell the submitter to fuck off. It does mean that they take on some liability of the claim turns out to be valid but again, they can determine that themselves and there isn't any abosolute safety from having to defend yourself against invalid legal claims in either case. Mozilla trying to benefit from extension creators (which provide immense value to the browser) while trying to offload all legal risk to the little guy is not exactly making me more confident that they are all that interested in protecting the open internet.

Now I haven't seen this claim specifically (has Mozilla posted it publicly?) but I doub the extension is actually infringing anyones copyright and this is instead about providing a way to circumvent coyright protections. AFAIK DMCA circumvention is not grounds for a DMCA complaint, which are for direct infringement of the claimants "IP" only.