"A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution."
keywords, peer to peer, no financial middlemen.
Now it gets interesting. Blockstream has a solution to increase bitcoin's capacity, which I don't think can be described as "purely peer-to-peer" and involving no middlemen at all. As a matter of fact, blockstream solution is to create middlemen that will process the vast majority of transaction...because they can't scale bitcoin (technical failure) or they don't want (political failure).
nobody bothered to correct me, so I'll have to do it myself. When I first watched this "Lightning Network Talk"... http://www.youtube.com/watch?v=8zVzw912wPo ...I got the impression that the layer on top of bitcoin would be run by big business and would be composed of relatively few 'big' nodes. However it turns out that, at least in theory, the LN is peer to peer and anybody can route payments for other peers. So maybe there's some hope for bitcoin...