I own it. The Clarisonic Mia IS cordless.
I don't know of any Clarisonics with permanent cords. Probably the reviewer is wrong.
Before I bought mine I read tons of glowing reviews. I do like having it, and using it. I've had it for three and a half months, and I like it very much.
Is my skin 100% better? Well, no, but I do feel that it looks pretty good most of the time. There are still days where I feel like my skin surface isn't the best but when it looks good, it looks pretty darned good. I'm over 45 (as a reference pt.) and I have a 20 year old friend who also got one, and he loves it too.