This is a great discussion! I've always thought that after the basic "how do I even do this at all?" concepts of programming, the next most important concept to learn how to wield and to perpetually sharpen is the "don't repeat yourself" principle. Huge swaths of software engineering literature is dedicated (explicitly or implicitly) to when and when not to apply that principle.
Your parent's comment addresses by far the best argument for the principle, which is that any time something is likely to change in a snippet, copy-pasting should be undertaken rarely and thoughtfully. With the recognition that nearly any given snippet is likely to change in some way, we can conclude that nearly any copy-paste is "bad".
Your comment is then a great argument against the thoughtless application of the principle, recognizing that yes, granted, nearly any snippet will change, but the required changes may well not be uniform.
Personally, I think it still makes sense to pull out shared behavior for the period of time in which it is shared. During that period of time, all you have is a guess that the code might eventually diverge. If there comes a point in time when you do want the code to diverge, it is straightforward to copy-paste it back out, if branching or creating a similar method with the differences is a worse option. On the flip side, if you haven't pulled out the shared behavior, and you discover that you want to change it everywhere in the same way, it is far less straightforward to go find all those places, or even be aware that you need to do so.
Another point is naming by purpose rather than behavior. To continue your example, it makes sense to ask why one method checks internally and the other externally? What different purposes do the different checking styles have? If there are good answers to questions like that, the methods can be named better, and it becomes less about memorizing name than understanding when to use which.
Of course none of this is at all black and white, and I think you're spot on that this is one of those craft bits, and among the most important!