I 100% buy they're using 1960s hardware. I've talked to some people who had to spend half their day on ebay trawling for parts to keep their ancient systems running. I've personally worked with medical offices still using 1970s hardware, it's not that rare. Many places have an "if it ain't broke don't fix it" attitude.
And it's an open question whether or not that attitude is better. A day or two of office admin time every 3-6 months is quite possibly more cost effective than hiring one of us for weeks/months/years to create a new system...
"a different group of mainframes would run an automated job that would harvest that data from the magnetic tape and load them up into more traditional databases"
