I think this is the critical miss @zeroflaw a vault on its own is not able to let you log in, cannot give you your data (it may have some small parts of some stuff) or do much really, like a single ant it is near useless, but in a huge colony then it all changes, just as vaults do in a network of them.
You are saying a server contains servers here btw. So a server is something made up of servers. That is conflating to an extreme degree. You will get caught in a recursive path to insanity if you follow that much further chap 
If this were the case then removing 100% of them would have no impact on your brain (absolutes again ).
At this stage, I am happy you call anything a server if you so desire, I doubt anything will change your mind and that is your prerogative. I do not think this is how people, in general, see p2p networks but if you do and by your definition, a p2p network cannot exist then great for you, if you contest it can but it is made up of servers and clients, then again that is your prerogative. Any further discussion seems fruitless really, so best leave it there. You can be the 1+1 cannot exist guy at presentations and be happy with your lot there, if you so desire. I have tried to help, but it seems this is a “faith” type debate now and you have made your decision.
I would say though, it won’t help you or the project to bring this up on every thread as it is noise really. As Feynmann said, it matters not a jot what you call something, it matters more you understand it at a deeper level than that.