As for the mather of the brain not being nessecery. first the treu headless zombies are part of the aftershock mod so i wouldn’t consider them cannon, as for the brainless zombie they are discribed as missing part of or there complere face so there is a good chance that the brainstem and cerebellum are intact the exact parts that govern motor function and automated movement. we know from corpse discriptions that anyone that losses more of there head is doesn’t revive so i would wagere that atleast these two areas are nessesery for revivecation if for no other reason that they regulate shit like breathing and heart beat which if these brain areas where missing would complicate revivecation by a lot. what does seem nessecery thow is a functioning nerve systeem since the blob doesn’t seem to be able to directly controle muscels or atleast not to the pressicion required to allow for fluid movement.
as for skeletons, they are not actual skeletons they are zombies whose skin has turned to bone so they do have muscels and organs to keep them moving, the only exemption to zombies not using muscels to move seem to be the skeletal dog and the hollow but they seem to be verymuch the exemtion than the rule with the blob instead prefering to use muscle as much as possible.