They don't really need the SSN. If they press for it, tell them you're on a visa and you haven't been assigned one. Verizon entered 123-45-678 for mine and it let them create the account :P
Be prepared to put up a $400 security deposit if you have no credit/ssn
I got that with AT&T, not Verizon though.
That is... odd. I'm pretty sure that was an exception, not the rule. You must have caught the customer service rep on a good day :)