You can burn, but not destroy armour stands by setting them on fire.
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is duplicated by 1
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This happens with paintings too. Is there a report for that, because this would fall under the same category.
I really hope this isn't going to be fixed. I made a post on the Reddit of how to make a campfire using this 'bug'. http://www.reddit.com/r/Minecraft/comments/2cx1hg/how_to_make_a_campfire_using_armour_stands_guide/
Most likely intended, since they are entities.