This hypersensitivity goes in both directions. One company may be worse than another at hiring, despite having an equal or better engineering department. Sometimes, you might just get bad luck. Your interviewer might not have had their coffee that day. Or their dog may have just died. Or you may get a guy who just proposed to his now-wife and is having the best day of his life. Giving a reasonable benefit-of-doubt mixed with a bit of critical thinking is probably the way to go, rather than resorting to hard and fast rules that will end up just making you conclude no company is good enough for you.
I don't understand this. As far as I can see, the entire goal of hiring is to have good workers, so the company with a better engineering department is better, by definition, at hiring engineers.
It might be that their hiring prowess comes in part (or in whole) from factors largely outside the hiring process specifically, something like "you get to work for Elon Musk", but their hiring is still better.
The only way to determine your false negative rate is to hire a bunch of "shouldn't hire"s and see how they work out.
Easy hire, easy fire is inhumane to people who believe that once you get one job somewhere your problems are over. Never-hire-because-we-never-want-to-fire is inhumane to people who interview poorly and do good work -- they're humans too. You can't win them all.