I'm 100% that walkers may pivot when immobilized in the shooting phase.
On page 72 is states specifically that when firing the walker you "pivot the walker on the spot" to aim its weapons at the target. Now, this is not movement, because it is done in the shooting phase, not movement phase. In fact, the rule later states more specifically that this pivot in the shooting phase does not count as movement. It is similar to a vehicle's free pivot in the movement phase, but not to be confused as the same action, so it is permitted since it is not a movement pivot (it is NOT in the movement phase as described on page 57), but a shooting pivot - again, like a turret. Essentially, Walkers have a 360 degree field of fire, they just have to pivot and stay put in the direction they shoot until they move or shoot again.
So, you will need to be carefull about which direction you pivot an immobilised walker because you are stuck in that direction since you can't pivot back after firing - exposing the side and rear armor - but I guess that could happen if you move or not.
Last edited by Eusebius Rex; 11-03-2010 at 11:06 PM.
Reason: bold and underlined for emphasis