The key point is that if you do work for a week to track down a showstopper only to have that thrown in your face and the only reasonable response is to "cover your ass" you are doubling your work. That manager should be fired for halving the productivity of their devs.
The main point of the article is that by "covering your ass" you are actually becoming a better developer, because the prose you write is plans and documentation and gives your thoughts structure.
Hence, your personal productivity (measured by what metric?) might suffer for this one task. However, in the long run you and your team gain productivity because of existing explicit documentation and plans.
A lot of plans and thinking goes into how to transition from the old to the new. Valuable for the "brief" period of transition but generally worth less once complete. This also doubles the time to deliver. Additionally, many times research and code analysis/review is needed to flesh out what needs to be done. Often times it's faster to make the changes when discovered rather than having to document what needs to be changed then getting the go ahead to change it. ("What did I change?" It's in the code commits and repo! Why do I need to translate it to English? Oh because my boss can't do my job...) This can drastically reduce delivery time. "What if there's a bug?!" What if there is a bug. We'll deal with it.
The key point is that if you do work for a week to track down a showstopper only to have that thrown in your face and the only reasonable response is to "cover your ass" you are doubling your work. That manager should be fired for halving the productivity of their devs.