You must remember most SS personnel have no clue how it works with immigration. They follow on screen prompts and enter things. Some like the person you experience is just a horrible person, there is no teaching them.
I see you already have it straighten out which is good. I was going to suggest going to a new office.
She was lucky to already have a ssn, there would have been almost no way to get it in her married name until GC or EAD. They need to match it up in the system and this hangs them up and instead of actually sending it in to verify they just deny it.
Getting that very first social really needs to be done before marriage if married for the love of all, do not ever mentioned it. So many employees think that getting married nulls the visa and will refuse to continue with the application. This is why we always tell K1 visa entrants to get that ssc before anything else.