that's nowhere near what -i- read in the original poster's post as far as teacher b's approach.
if an instructor for a beginner teaching an hour lesson spends 15 minutes showing a transcription of a song, to put in the student's notebook for study, and discussing the theory behind the song, and then focuses the rest of the 45 minute lesson on helping the student develop their ear by listening to a recording of the song, and develop their techinique by trying to play the parts in the song, i would find that as an excellent lesson for a beginner, and well worth their money.
an absolute beginner is going to have the hardest time - and need the greatest instructor assistance - with the simple mechanical aspects of playing. they've never moved their fingers that way before - they might not have even held an -instrument- before. that's going to take the lion's share of the lesson just to get someone's finger/hand/arm control developed sufficiently to properly execute a note on the instrument.
anybody who has been in school for a more than a day is going to know how to -learn- theory. for the first few lessons, take home materials are going to be pretty self-explanatory, and going over the fundamentals of music theory is going to be better accomplished by the -motivated- student on their own time, to be quizzed at next lesson.
when i was a beginner (25 years ago

heh) , if my teacher spent 45 minutes of my hour lesson going over scales and modes, when he could have given me a handout and let me read it on my own, at the expense of him showing me the mechanics that i did not know and could not teach myself, i would be pretty aggravated.
like i said earlier, a balance between the "why" behind the music, and the "how" of the music, is the best approach, i think, for teaching a beginner. after a while, once there is actual -playing- being done by the student, then the mechanical aspects of the playing (i.e. what i am taking to be what the teacher b is specializing on) can be lessened somewhat in favor of more theoretical concerns.