What is the adult student looking for in lessons? Classical rep, playing favorite songs on the piano? It depends on what they want. I have an adult student who can read music, but based on what he wants, I'm using my own method and teaching him what he wants to play. Basically he wants to play songs he knows, so that he and his family can sing along, so I work a lot with chords, both with reading lead sheet and recognizing function for transposition purposes. He seems to like what we're doing.
Adult books - not sure about the regular Alfred adult book. I think I remember some fairly kiddie pieces in it that don't appeal to adults.
The Alfred piano for group classes is good in that it is comprehensive - technical exercises, reading examples, scales/chords/theory, harmonizing, and repertoire. It is intended for group classes, but could be used solo I suppose.
Faber adult method I also like, but it moves at a slower pace than the Alfred. We used the Alfred at school for music majors who were not piano majors but had to pass proficiency exams.
I am not familiar with the book you mentioned. I used one this summer, but don't remember who did it - only remember that the cover was purple, I did NOT like it.