Traditionally the Sunday strips have nothing to do with the story line in the weekly strips. Therefore, its my conclusion that wally's natural laziness and indifference is the real reason PHB does not want him being in charge.
In the last strip, Wally told PHB his dream was to be like PHB. To PHB this meant, 'I could be taking your job in the future.'
So PHB sees Wally as a threat, if he makes Wally acting manager, Wally might just put on a better show for his boss, and take PHB's job.
This is what Wally wanted him to think all along - being acting manager would mean more responsibilities (however slight) but the same pay. As a result of 'manipulating' PHB, PHB doesn't want to assign Wally any responsibilities, for fear of him looking good to his boss.
Thus, in a situation where Wally would normally be called upon to do something, he's ordered to leave work instead.