Whenever I've had a situation like this I do it in strict confidence and don't put it in their face, almost always say to the effect "hey I think I found something, can we grab a room" and go straight to the whiteboard and begin drawing, and use language like "so check this out... I'm a bit worried about this, what do you think?" I let them arrive at the same conclusion I did, or at least start a healthy debate. The great thing about doing this is sometimes you are wrong, maybe not technically, but there are other considerations that went into the decision that you're not aware of.

Also I've learned to not overstep my own bounds, when I have issues with another dept I don't go rogue and knock heads, but go to my own supervisor and ask if they can talk to the sup in that dept and get back down to their respective staff. The only exception to this is for time critical issues, I'll send an email blast to all involved parties first, then walk around and talk to people - ask them if they have time in their schedule to look at something, if not who else they might be able to introduce me to, etc.

Basically everything I learned about dealing in a corporate environment was through making tons of my own mistakes and watching the tv show The Wire and following the "Chain of Command" and seeing quite a bit of Jimmy McNulty in myself :).

All this said, the biggest blowup I ever had was only a year ago, it cost me a relationship with a director a couple levels above me, and it was the result of actually doing something that probably saved the company a cost in the 6 figures for only 3 days of work... it was a combo message of "great job... and you made me look like a fool". I totally get it, I would feel the same way if I were him. But it was still the right thing to do, and sort of a signal that perhaps the corporate world is not for me - or at least that one particular environment. YMMV.

It's all in how you do it.

Humans are fundamentally social animals, hardwired for status. As a nerd that was mainly invisible to me early on. Two books that really helped me see how it works in humans are Chimpanzee Politics by deWaal and Impro by Johnstone (in particular the section on status transactions).

If you correct somebody in a way that costs them face, they will trust you less. E.g., publicly demonstrating that they're totally wrong in an important meeting, especially when done with irritation and contempt. You can have the same discussion privately in a fashion that's caring and supportive and you'll be trusted more because you've demonstrated that you're an ally.

I would like more detail in that anecdote as well. Anecdotes can be powerful teaching aids if there is enough information about the people in the anecdote and the situation.

I'd imagine that the writer's arguing back and proof that the manager was wrong made the manager look bad in front of other people. Corrections of fact might be better in private. I'm just guessing though.

It felt a bit like the lesson is "be servile whenever possible". But maybe I'm misunderstanding the author.