That's not true. You may want to have entire block chain - if you wish to verify every block. Miners need to do so, to be sure they don't build their blocks on top of invalid blocks. Regular people don't require that and can trust some web wallets or light clients like Electrum, that store only block headers and keep track of personal keys, but do not verify all the transactions.
It is true if we define client as "client which implements BTC protocol". If you define it as "random internet strangers I trust with my money" then of course it does not require the blockchain and also does not provide any of the strong guarantees from BTC. Even for Electrum which does not have your private keys, you are still trusting what it says the blockchain contains. If subverted this could for example lead you to believe that someone had sent BTC to your wallet that were not actually in the true blockchain.
I didn't say I don't need to trust anybody. I have to trust even the full client: I need to validate the checksum, make sure I don't have viruses and keyloggers on my machine, I have to trust my backup system and have to trust people who understand crypto better than me.
Everyone must trust someone, there is no clear line in the usability-vs-trust balance. I'm perfectly okay to trust a web wallet on blockchain.info small amount of bitcoins because they do a very good job with their iPhone app and SMS notifications. I'm also okay to put some of my money into Electrum and some - in Bitcoin-QT. And keep some on bitcoin-central.net in case I need to sell BTC for fiat quickly.
Given all of that, it's not fair to say that "the true" client is this one, while all the others - are considerably different. For people who value their time, it's important to be able to sacrifice some trust for usability and vice versa. If we would always tell them that they must use the full client, we are just imposing our personal tradeoffs and do not respect theirs.
