Spot on. When I relocated to the US from Europe, it was impossible for me to open a bank account, rent an apartment or get a cell phone without an SSN.
When I explained that to people at the SS administration, they told me that an SSN can never be a requirement to obtain any kind of service. In reality, it's simply not true.
Under no circumstances, outside of tax purposes (employment, banking, etc...) can you legally be required to provide an SSN in the united states. Any time I've been "required", I've put up a fuss, and eventually been granted equivalent avenues to provide assurance of payment or reference checks. In most cases this involves a three to four month deposit on the service. Annoying, but given that the organization is entering a commercial relationship with me without knowledge of my credit worthiness, bearable.
I detest these centralized government tracking systems on my activity, and hope that this next attempt on a national ID is quickly defeated.
