However I've heard it said that the above assumption is significantly undermined by a "common culture" shared by programmers.
Said by whom?
And no one was talking about software attaining perfection. Merely that the probability of two completely separate pieces of imperfect software prohibited from sharing any common logic coming up with the same computational error is extremely remote.
You're just going to have to trust me that the only thing that safety-critical software development has in common with what we, the public, encounter as 'computer software' daily is that it all works on binary logic eventually.
I cannot stress enough that the development process for saftey-critical real-time software is unique in the industry.