Did the dialog specify that the phaser control room was on deck eleven? From the external views the phasers (or at least the emitters) would seem to be on the lowest saucer level, but the control room wouldn't necessarily have to be immediately ajacent to the phasers themselves.
The dialogue is not specific, but according to The Making of Star Trek "deck 11 contains the ship's phaser controls and other related equipment and facilities...primary control facilities and equipment are located on deck 11."
The visual evidence comes in form of the phaser coolant, IMHO.
As seen in "Balance of Terror" this coolant gas is lethal and I believe that nobody with a sane mind would run such coolant pipes through the populated areas of the ship, but keep the coolant confined to a (small) area and right next to the equipment that needs such hazardous coolants.