Yes. That's right! But is blockchain.info really secure? It is web wallet, so it might get hacked any time. IMO it is better to use Mutlibit HD which is a little better than Multibit. Remember, it is in Beta stage, so if you want a stable one, you can use Multibit. If you can't install Java, you can use Electrum.
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If blockchain.info got hacked or shut down without warning one should still not lose their bitcoins as long as they've followed the fairly simple procedures to keep a hold of their private keys. Nor can the attacker necessarily get the user's bitcoins because (in theory) blockchain.info themselves do NOT have the private key.
What an attacker, or a corrupt management, could do would be to start sending out a bogus javascript which would steal one's password and thus make it so that blockchain info could access the private keys. As I said earlier, I would hope that this form of failure would effect relatively few people before it was detected.
The most legitimate problem with blockchain.info is, in my opinion, that the javascript interpreter which is normally part of the user's browser could be exploited. Or other exploits of the host platform could present problems. Naturally this could impact things besides web-wallets of course though.
It is worth note that historically most 'web wallets' did NOT follow the model pioneered by blockchain.info. And of course as we know an amazing number of such 'services' ended up stealing the user's Bitcoins. Surprise, surprise. I would not consider a web wallet that did not meet or exceed blockchain.info's standards.