I don't think you have to worry. It would only facilitate stolen accounts if AS were to sell our details or if they were stolen from AS.
AS is a business and depends on the trust of its customers (us) so it wouldn't do them any good if their security was anything but excellent.
I haven't been a user long, but there are people here who have been with AS for years and they are still here. I would guess that their accounts haven't been stolen as a result of using the service.
In general, I would say that on the web, never do anything you're not comfortable with. If you don't feel comfortable with using AS, then you don't have to....but I personally feel you would be missing out on a lot if you didn't. JMHO!
SuperSqueaky