I don't think that's the story, again, I think you're overemphasizing a particular kind of book index you're familiar with. Here's usage of 'direct' and 'inverted' index from 1903 that I just googled up
I think it shows quite clearly that your theory that Information Retrieval nerds just got confused/misapplied a particular kind of book index is inaccurate and that IR nerds have been around for longer than one might think.
- someone introduced the term "inverted file" for this sort of thing (which is sensible terminology)
- later people started considering these things to be a sort of database index
- so they started saying "inverted index" without paying attention to what that implies as an English phrase