This is absolutely not an issue of embedding. And for that matter, since the fonts you are discussing are the old, legacy Type 1 fonts, there weren't any embedding permissions flags in the fonts to concern yourself with.
The real issue is that for standard Windows applications that don't enumerate their own fonts, font families that have more than just the four regular, italic, bold, and bold italic typefaces are fairly problematic. In order to ensure full compatibility with all applications, font vendors typically do some fairly strange mapping. This mapping is indeed inconsistent with InDesign, Illustrator, and Photoshop which show you the full and proper font names and styles.
Acrobat, for better or worse, for the text touch-up editing and forms edit capabilities, has chosen compatibility with the typical enterprise applications for font selection on the basis that these activities are more likely to be performed by Office users as opposed to graphic artists.
To your point about the full Avenir family from Font Folio 9, the mapping is as follows:
Avenir 35 Light ￫ Avenir 35 Light
Avenir 35 Light,ITALIC ￫ Avenir 35 Light Oblique
Avenir 45 Book ￫ Avenir 45 Book
Avenir 45 Book,ITALIC ￫ Avenir 45 Book Oblique
Avenir 65 Medium ￫ Avenir 65 Medium
Avenir 65 Medium,BOLD ￫ Avenir 95 Black
Avenir 65 Medium,ITALIC ￫ Avenir 65 Medium Oblique
Avenir 65 Medium,BOLDITALIC ￫ Avenir 95 Black Oblique
Avenir 55 Roman ￫ Avenir 55 Roman
Avenir 55 Roman,BOLD ￫ Avenir 85 Heavy
Avenir 55 Roman,ITALIC ￫ Avenir 55 Oblique
Avenir 55 Roman,BOLDITALIC ￫ Avenir 85 Heavy Oblique
This information comes from the README.txt files in Avenir 1 and Avenir 2 directories of Font Folio 9. Information for such mapping is in the README.txt files for other families as well.
Hopefully this solves your issue and gives you some background as to what is actually going on here (even if you and I don't particularly like it)!