Rewriting Results with Taxonomy Term is Rather Confusing

So, when you rewrite your results using a Taxonomy Term and try to either select "Link this field to the original piece of content" or "Output this field as a link" with the [path] token, the Taxonomy Term link will take over and will link to the term page no matter what you do.

Except.

If you select "Strip HTML tags" under the rewrite results heading and have "Link this field to the original piece of content" checked, it WILL change the text of the link to the taxonomy AND link back to the original content.

I found this completely by accident and after a cursory search on the issues, I decided to add it here, if only so that someone doing searches for the same thing in the future will find the solution.