But the DMCA is the only legal mechanism for demanding swift action from a registrar/hosting party without the involvement of a judge, at least FAFAIK. So if this wasn't a DMCA takedown, then the registrar was acting completely of their own volition and should be liable for all fallout.

No, sadly it's not. These are private companies.. if you write to them and tell them to take a site down for "reasons" and they think the "reasons" are good enough, they'll do it.