But with this mindset, do programmers then avoid non-programming activities where errors can be serious/fatal?
In my experience, the programmers are closest to the technical controls in the organization. In matters of compliance and security, the programmers will often play a key role in documenting existing practices and suggesting ways of meeting requirements.
Maybe you had something else in mind.
Programmers don’t exist as a distinct species with a special mindset. And few programming bugs have anything close to serious consequences, compared to installing a child’s car seat, for example.