The story, from Discovery, explains that stuffing the mouth with a large stone did not apply to all bodies, but only those of really scary people, like murderers, or those who died strange deaths. Stuffing their mouth with a stone would ensure that they would not come back as scary zombies.
Naturally one is immediately reminded of #5 in the Testament of R. Yehuda ha-Chassid, which says
or, "When they bury a woman who had consumed children, if they see that her mouth is opened then she will definitely continue to do it during the first year after her death. So they should fill her mouth with dirt and this will be effective so that she will not cause further harm."
There is certainly no doubt that if you stuff a corpse's mouth they will not come back to haunt anyone.