I've dealt with "complex" systems for my entire 40+ years working life. Even the smallest of businesses give thought to what happens if the "computer says no" ever since the earliest days of computers in the 80s, like Commodore PETS. A small private business simply couldn't survive a catastrophic failure like this, so they build in alternative systems and backups.
Even in my own small practice, I'm fully computerised, but we still have basic/simple paper files so that we can (and have done) continue to operate with system failures, power cuts, etc. OK, not at full 100% productivity and efficiency but we could still do our clients' weekly payrolls which we had highlighted as the ultra important work we do so we had robust recovery systems and manual alternative systems in place. If a tiny little "hick" firm can do it, then huge firms with huge resources can do it!
When I worked in industry as financial director, hundreds of staff, multi million pound turnover, everything was computerised, ordering, stocks, sales, production planning, etc., but we still had backup/disaster recovery plans that meant we could continue if the systems were down/power cuts etc. Again, not at full capacity etc., but if an order was critical and the customer needed it at a particular site on a particular date, we knew we could do it, one way or another. We were in the Worldwide Oil and Gas Industry and failure to supply a critical component at the right time was critical - our contracts put us on the hook for huge damages/compensation if we didn't - so it was baked into our thinking and systems to make sure that whatever happened, we'd manufacture and deliver on time! (Damages/compensation could be tens of millions if our failure meant a gas or oil platform couldn't start up on the appointed date!).
I have "the conversation" regularly with my clients - I constantly bang on about back ups, duplicated systems, paper based backup reports, etc.