The fact that you can get Linux kernel developers who rail strongly and vehemently against compilers because the compiler optimized it against what you said, which wasn't what was wanted, strongly suggests that it's not a matter of precision.
More specifically, people generally have a vague idea of what they want. While you could explain a fully precise mathematical model that corresponds to that idea, people don't really have a good way to know if the model is correct or if there is some hidden corner case that causes problems. So they accept the model until they find one case where it was wrong.
It's hard to impart the true understanding of just how much details a real-world problem has without making someone try and solve some real-world problems.
More specifically, people generally have a vague idea of what they want. While you could explain a fully precise mathematical model that corresponds to that idea, people don't really have a good way to know if the model is correct or if there is some hidden corner case that causes problems. So they accept the model until they find one case where it was wrong.