I think I understand your question. Let me try to answer.
Assume:
the online wallet operator stores only an encrypted version of your private keys
key decryption and transaction signing is done on the client side, without giving the operator access to your unencrypted keys at any time
you have a strong passphrase on your private keys
the client-side software is correctly implemented and not compromised
Then an attacker or dishonest employee who gains access to the operator's data will not be able to spend your coins.
They could conceivably delete the operator's copy of your encrypted keys. If you have a backup, this won't really bother you, since you can decrypt the keys and use them to spend the coins yourself. If you don't have a backup, then the coins may be permanently lost: neither you, the attacker, nor anyone else would ever be able to spend them.
They could also threaten to delete them, or demand ransom to return the encrypted keys to you. Again, if you have a backup, you can ignore their demands. If you don't, then they have you over a barrel, and you might be motivated to pay them a sizeable fraction of the value of your coins to get the encrypted keys back, because otherwise those coins would be lost to you.
This is nearly impossible to understand. If anyone takes control of your wallet it will always be spendable. The point of a backup is to keep a second copy of your wallet in a safe place for circumstances where you lose your wallet. – John T – 2014-03-22T19:36:01.937
I’m a newbie. It’s not hard for me to believe that the answer to my question might be “no,” but how is the question “impossible to understand”? They do indeed claim that it is safe because they “encrypt everything.” – WGroleau – 2014-03-23T01:31:40.437
What exactly are you asking? I have trouble understanding what you mean :( – Joe Pineda – 2014-03-23T01:35:03.850
In many languages, including English, a question mark on the end of what would otherwise be a statement, implies “True? or false?” I will make it explicit. – WGroleau – 2014-03-23T01:38:11.683