throwzone

A situation cam up in our game yesterday. New pitcher for opposing team came in to pitch....runners on all bases. After his warm up pitches, the said pitcher was in the stretch position.....then came to a Set position. Hands are still...then catcher gives pitcher the sign for the pitch to be thrown. The pitcher shakes no, no then shakes head yes...where he then proceeds to pitch. I was always under the assumption that you must get the sign from the catcher.....with runners on base.....from the stretch position, NOT the Set position. I cannot find a rule for this but game umpire said no balk that it is legal. I brought up about pitcher's ability to essentially Quick pitch the hitter. I asked an umpire friend of mine who said it is a balk following under deception. I am confused on how to interpret whether or not there is a specific rule...what the section of that rule it falls under....and should a Balk have been called. Thank you for any assistance! Jim