There were ways around it
If two digits were stored for the year, and it didn't have any years earlier than "65" for instance, you could add a bit of logic to do "if year < 65 then fullyear = 2000 + year". Before someone says "what about birthdates" anything that was written in the dusty deck era would have had to assume the possibility of people being born prior to 1900 so would have have had other issues with a two digit year.
Of course Y2K provided a great excuse to rip out the old equipment, if someone had fixed it then you'd never get upper management to agree to replace it. I often wonder how much of the economic boom in the late 90s was due to Y2K spending - and how much the recession that had already begun prior to 9/11 was due to "all our equipment is brand new, we don't need to replace anything".