I'm not disagreeing with your conclusion. All I'm saying is that I'm just parroting these things without actually verifying them - and so are you. If flat Earth gets you all excited, I can also explain the concept with Pythagoras' theorem.
I never did a formal proof of it, yet I just use it because it works and I'm pretty sure it's true. Someone else proved it and I'm just parroting that without ever even having bothered to read the proof.