They're signatories to the Berne Convention[1] which gives you automatic copyright on "every production in the literary, scientific and artistic domain, whatever the mode or form of its expression" and also gives you control over rights for "the right to make adaptations and arrangements". Which I would understand to mean they can't say "copyright is void because of XYZ" - it was created, it is copyrighted. I'd imagine WIPO would slap this down.
> As far as I know the US copyright system is very different from that, where you have to register or apply
Since they're signed up to the Berne Convention, copyright is automatic but apparently there is an allowed "requirement that the right holder of a “United States work” have registered the work before initiating a lawsuit" (from [2])
[1] https://www.wipo.int/treaties/en/ip/berne/summary_berne.html
[2] https://www.mediainstitute.org/2009/10/20/borderless-publica...