I would call it a distributed centralaised ledger. This may seem an oxymoron but the point is that there is a redundant network of ripple "servers" (not be be confused with client nodes) however the server source code remains closed source and only OpenCoin or agents of OpenCoin run the servers.
I would liken in to a private content distribution system being distributed but still under centralized control. The advantages are no need for mining, no need for proof of work. What the centralized network says is the status of coins is the status with no appeals or overrides.
There is no need for "proof" because all servers are trusted authorities. They are all run by the same entity and there is no reason or scenario where they will provide conflicting ledgers. At a high level one could say the purpose of "proof of work/stake/etc" is to resolve conflicts in the consensus. There will never be conflicts in a distributed centralized network.