Not always true. If you are married, make sure you freeze both your and spouse's SSN. About a year ago, someone had stolen my wife's identity and had a fake driver's license and walked into my bank in another state and withdrew 11k over the course of a few days.
We did the whole credit freeze thing through all the bureau's and when setting up new accounts at Chase, they offered me a $500 sign up bonus for their credit card, direct deposit, etc. I said it wouldn't work, but go ahead. 30 second's later I was approved. Turned out, the freeze was only put under my wife's name and SSN.