I can see that there are similar services, but not the same. They all don't allow you to input your own address.
It would also be even better if the funds could be sent through a mixer. Is there also a bitcoin mixer that has permanent mixer addresses, not like bitmixer's 24 hour address?
If you use an online vanity address generator that doesn't use the split-key method, you are correct.
If you use a split-key service, like shorena's, you are safe... If you're like me, and don't trust other people at all, you can just use vanitygen and generate an address yourself. This way you know your coins won't get stolen, since you're the only one holding your private key