Seems that the generation that went through the depression (who would now be approaching 100) had that mindset. On several posse-commissioned hunts I've done for people, the story was earily the same: Typically someone (their father, grandfather, etc...) was thought to have buried stuff , and now the family was looking for it. And when you put the story together, get the age of the patriarch who's passed away, it's seemingly someone who'd gone through the depression era (when banks had failed).
Another few times it's been younger people though (persons who came of age in the 1950s or whatever). So perhaps some people even-to-this-day still do it ? And while you say banks aren't fail-safe, yet they are insured, which is something that wasn't the case during the depression. Sure some people don't put much faith in the "federally insured" signs/notices at all banks today, but .... just sayin', the era of "not trusting banks" is as much present now, as it was in our grandparents generation.