Depending on what you mean by "in a decentralized fashion" the two aren't mutually exclusive. Many bitcoin clients, like Electrum, are distributed, non-centralized, but rely on the existence of SOME copies of the entire blockchain somewhere, but only verify back a fixed configurable number of blocks themselves when sending and receiving money. I suppose there's a minor degree of "trust" involved there, but I think the number of full nodes talked to is probably also configurable, so it would be pretty hard to fool the client, I think equally hard or harder than other kinds of double spend attacks.