Welcome to the forum!
Guessing this references parsec for total order consensus. Maidsafe moved away from that, still use gossip in some capacity but data and network changes are guaranteed eventually consistent by utilizing CRDT’s in novel ways. You are right that this is a totally permissionless network.
I’m no expert but what I can grasp is extremely interesting stuff that I don’t see much of elsewhere, especially not the total network design.
Maybe I could tap @dirvine for a solid answer when he has a free mo. I would also check out the Weekly Update and the Safe Network Primer which are excellent resources that you can gain a lot from.