Presumably when they are on fire, they are spending all their effort seeking shelter from the sun. But if they're in a box with no path to shade, they'll just wander aimlessly, they won't shoot the player, and the player can't be hurt by touching them.
If you try REALLY hard, you might get a skeleton on fire to shoot you once, twice if you're really lucky. But most times I spawn a skeleton, they won't shoot you even once, even while they stare you in the face repeatedly.
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Comments 2
This seems to be resolved in 1.8.7
Skeletons will actually stop and shoot at you for a long time even if they're on fire. Likewise, when you give them helmets, they don't seek the shelter of shade before shooting you.
Not sure if anything changed of if I was just using different test conditions. In any case, this ticket can be closed.
Also if you put an item in their head slot so they aren't flammable, they still won't attack the player until they get out of the sun.