> invalidate my argument that they are alike in the specific ways that I outlined

Basketballs and apples are both round, so they're the same thing right? I could eat a basketball and I can make a layup with an apple, so what's the difference?

> programmers who treat the compiler as a black box (ie. 99% of them) see probabilistic outputs

In reality this is at best the bottom 20% of programmers.

No programmer I've ever talked to has described compilers as probabilistic black boxes - and I'm sorry if your circle does. Unfortunately there's no use of probability and all modern compilers definitionally white boxes (open source).