you also need to have countermeasures for key loss and revocation for breach, and it essentially also kinda means it needs threshold signatures which are easily doable with bip-340 schnorr signatures, but you need a scheme to pre-state signatory pubkeys as tags before any signatures are applied to the event
it's a whole key management protocol if it is to really be secure, and that *requires* that the organisation *must* also be caching all relevant events in order to prove authority and maintain this for events as they propagate (so they have to broadcast them)
which comes back to another of my hobby horses which is the idea of broadcast vs narrowcast event types and the informal notion of authoritative archivist relays - the signatures are secure, but if the events are lost the authority is too