Fire Resistance does not extinguish mobs

I thought that throwing a splash potion of Fire resistance at a normal burning Skeleton (because of daylight) would put out the fire (causing the sporadic one frame burning animations found in Pigmen & other mobs with natural fire resistance). It didn't. The Flaming Skeleton doesn't seem to be taking fire damage under the potion effects, however. It still thinks it's burning, and its AI doesn't shoot at my snow golems that are throwing snowballs at it.

It doesn't matter if the Fire resistance is applied before or after the Skeleton catches fire.

This is also true for Zombies (normal and villager), with the exception of the babies (which don't seem to burn without potions anyways.)

EDIT: works with any flammable mob that steps on a flaming block.