Forum:Priority in the battle phase

I'm basically having a big issue with this flowchart Breakdown of the Battle Phase. I have 2 respectable judges whom I trust completely both telling me that when you enter the battle phase, you have priority to declare an attack before your opponent could activate an effect such as Book of Moon. They say that yes, cards can be used in the Start Step, but the Turn Player still has priority to attack because the steps of the Battle Phase besides the battle/damage steps during battle aren't really important and play out at cleanly as the rulebook tries to describe it.

Said flowchart has no official rulings source and I would agree with what these judges are telling me over that. In OCG too.