I was surprised that you said we may use any Social Security office. When I visited our local office, people who lived nearby but in another county were refused service. They waited a long time for their number to be called, but then the staff (who are behind glass, as if selling tickets) would then just point to a sign saying that they must use their local office. The security guard at the door was not willing to direct people either, but just pointed to a terminal to register for a number. It was a worse (more rude treatment) experience than the DMV, and not what a person should receive after paying thousands of dollars in taxes for many years.
I'm surprised to hear that the office you visited actually had a sign telling people that they must use their local office, and that they refused service to someone. That is contrary to formal Social Security policy, as is outlined in this section of their operations manual: https://secure.ssa.gov/apps10/poms.nsf/lnx/0200904064.
I'm also sorry to hear of the rude treatment that you experienced when you visited your local office. That shouldn't happen anywhere, although long waiting times are frequently unavoidable due to budget cutbacks. You may want to consider contacting the office of your Congressional representative(s) to inform them of your experience.