Seems like I've read that if you won't give a ss # the provider "generally" won't let you order service, unless it's prepaid, that's the main reason asking for the ss# is to pull a credit report(s).
I believe the "no cc rule" is a state law in PA & MA, I think it means the provider can not require a cc in order to begin service, I'm guessing the provider would ask for a a debit card # or checking acct # as a means of having some security they'll get paid.
I don't object to giving my ss# if I'm getting a credit card, loan, establishing a new utility acct, etc.
I think that is better than putting a deposit down, not getting the best loan rate, etc. I'm more concerned about the non-financial operations (such as doctors, dentists, employers, etc) having my ss#, too many people have access to it that could do a lot of damage.