Well you are still downloading the whole chain just some of it via bittorrent.
FYI you can avoid the download entirely by using alternate clients like electrum (electrum.org).
About your last post, it's not just about verifying that someone knows the blockchain. It's about redundancy. A decentralized system is naturally redundant. If one, two or even twenty thousand computers with the blockchain go offline bitcoin can still continue to function because the remaining computers have a complete copy of the blockchain.
As far as speeding things up go they are working on it. They want to implement a separate chain that contains balances only:
http://codinginmysleep.com/ultraprune-in-plain-english/