Reel to Reel - Half Track - Quarter Track

I currently own a TEAC A3340 and a TEAC A3340S.  I purchased one of those analogue productions ultra tapes  (I am assuming since its uni-directional its a half track tape.) and noticed that: the right channel volume was lower and the phasing was thrown off toward the left. However, when I played it through tracks 1 (front L) and 4 (rear R) the volume and phasing issue were corrected. The sound was excellent, but I can't help thinking that considering how expensive these tapes are am I getting the full benefit from a 1/4 track machine or does one really need a 1/2 track deck to get the best sound?

Another question is how can a 1/4 track playback head even play a 1/2 track tape?  I must be missing something here, any enlightenment would be appreciated.

Thanks