The "louder" seems associated with piano music. I can only imagine that a pianist would stress a note to keep the sound from fading away too soon--thus an attempt to make the note and the one following sound more legato.

I learned what you learned, Steve. But one choral director I worked with was taught that a singer should push a little on the note with a tenuto mark, to make it a bit stronger, louder. Probably his teacher is teaching all his conducting students that way.

We may need to add footnotes if we want to avoid tenuto marks being played or sung louder.