Re: "Cargo cult science is a bit harsh for most."
Could I have checked that when I bought it? Yes, of course, but you assume that the company selling right angles sells right angles, and not sort-of right angles. Do I "deserve [my] five minutes of shame"? I am not sure.
No, you don't deserve shame, but you have learnt a valuable lesson: A careful workman never assumes; he checks. First building site I worked on I was taught two things:
Measure twice and cut once.
If you've got time to do it twice, you've got time to do it right the first time.
Easy way to check a carpenter's square is to draw a line while holding it against a straight edge. Flip it and draw another line a smidgeon* away from the first. If the lines are not parallel, the square is useless.
* Technically, a red cunt hair, but if there's no red cunt available, a smidgeon is near enough.