I think a part of the problem is that in addition to being a well regarded principle with a good pedigree, "DRY" is both catchy and (unlike SOLID or similar) seems self explanatory. The natural interpretation, however, doesn't really match what was written in The Pragmatic Programmer, where it doesn't speak of duplicate code but rather duplicate "pieces of information". If "you are okay with functions drifting apart or the cases they handle are allowed to differ" then the two functions really don't represent the same piece of information, and collapsing them may be better or worse but it is no more DRY by that definition.
I've tried to counter-meme with the joke that collapsing superficially similar code isn't improving it, but compressing it, and that we should refer to such activity as "Huffman coding".
It's also worth noting that the focus on syntax can also miss cases where DRY would recommend a change; if you are saying "there is a button here" in HTML and also in CSS and also in JS, your code isn't DRY even if those three look nothing alike (though whether the steps necessary to collapse those will very much depend on context).