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.