Let me see if I understand this correctly...

Fresh off of the cat posting, let's talk inter-mammal workplace relations.

In case you wonder if there is some deeper meaning in yesterday's cat posting, we can neither confirm nor deny that you read it to mean that a feral yard cat can exhibit more empathy and kindness than the majority of mammals currently in charge of the planet. 

Of all the strategies, which in reality are merely tactics, of dealing with obnoxious co-workers or bosses, one of our all time favorites is the use of Let me see if I understand this correctly...

The blogster has used it in place of the slightly more honest "Look, you moron..."

The number of argumentative co-peeps at work has astounded the blogster from day one, which was somewhere around age sixteen.

The capacity of intelligent workers to set aside all logic in their pursuit of personal animosity outstrips their professional achievement more often than not. We are not offering an example, you will have seen some around you.

If you have not, ask yourself if you are lucky to have such a great workplace and wonderful co-workers.

If you answer this question with no, go back to the start of the paragraph "The capacity of intelligent workers...." and try again.

Anyhow, the number of web sites and self help books on conflict management are legion, but you can hardly look up advice in McFeelgood's Seven habitats of the healthy worker every single time there is a clash.

A handful of tools is what most of us, especially the blogster, can muster at any given moment.

Let me see if I understand this correctly... is one which has put out the flames of resentment more than once when a nonsensical request or a dumb order (usually also masking as a request) popped up.

Lead in your response with Let me see if I understand this correctly..., then state your perception and views. 

A simple example could look like this. Say, you are purchasing toilet paper from a group of different contractors. Every few months or so, you ask for new estimates based on your changing bulk supply needs. In the run-up to Christmas, you employ more people, hence, a lot more shit goes down. Departments report their forecasts to you, you turn them into one easy number, that's it. Okay?
Then, one day, your boss wants you to email him the details for each department before you ask for tender.
You remind him that the details are stored on the sever CrumpleFold and the links to the documents are in the purchase order system's comment field. He knows that.

He lobs the magic word "insubordination" at you.

You go: Let me see if I understand this correctly, you know the links are in the PO system, you have access to it, and you have used the links in the past without problems. This makes me wonder why we need an additional step, which sort of defeats process streamlining.

This way, you hold up a mirror, you listen, and you offer him a way out. The clause "if I understand correctly" provides him with the opportunity to tell you that you don't grasp the reason or sense of the request.
It also invites him to re-phrase it -- after all, if a subordinate or colleague fails to understand something, you try again, right?

Another example: A colleague emails you a question, you answer it, he gets his task done and thanks you.
The colleague's request was mundane, nothing to it. Having the same pay grade and - on paper - the same skills as you, the co-worker should have known this but it is no big deal. Maybe he had a bad day.
A day later, you get an email from the manager of your boss: "In the future, please go through channels with any requests for assistance."

This reaction can be a huge red flag, and there is no golden rule on how you should react in turn.
Why would this manager send out this email to you and, of course, your immediate manager? It is conceivable that he is trying to build a case for dismissal of that co-worker, isn't it?
On the other hand, you did not blab about the initial request, so the co-worker himself must have told his manager, or even the manic mailer, which indicates that the co-worker does not feel under threat or is covering his ass.

Next time you meet the boss of your boss, you could do a Let me see if I understand this correctly... 
Your counterpart surely has used the standard "team" and "help each other" boilerplates previously? Use them. Then add a carrot, along the lines of "I planned to add an entry in the knowledge base", or "I find it helpful to get an idea of the problems we face on a daily base".

If the man merely repeats the go through proper channels line, congratulations, you have a second tier manager who will ensure that his seat is safe and through you and others under the bus as needed.

Do not overuse Let me see if I understand this correctly... because in starting every other conversation with it, you provide a vicious co-worker with a line of attack on your intelligence and job skills: this guy always has to ask for clarification, what's wrong with him.

However, you should be out of that department and have a new job before it gets to this level of fun.