Tell them you want your service billed to your credit card account, thus they don't need an SSN.
I went through a similar situation a few years ago with a text pager and Ameritech. Paid for the pager hardware and a years service IN ADVANCE using my Credit Card.
Person at the branch wanted my SSN - told them there was no reason as I was paying for everything via CC. They claimed it was their "policy". I declined and pressed it to higher management. Each time I spoke to a person that couldn't explain the reason I requested to speak to their manager. Kept a log of names, numbers, titles, etc.
I escalated the issue to a VP of operations at Ameritech and they acknowledged it should not have been required and offered to "fix the problem".
It was resolved.