Well, this was solved quite well by trapped chests! I'm very happy with that fix. Now you can even have single chests side by side.
I certainly love that you can open chests with glass, glowstone, slabs, stairs, and other solid blocks yet transparent blocks, but I think the lid opening into other blocks makes it a bug. Sad, but that's the way it is.
Strange, seems more like a bug to me, since you can open stacked chests (like Daniele said), as well as chests with transparent blocks above them.
If that can be considered as a bug, MC-378, then I'd say this is a bug.
If the chest stacking were to be fixed, then I'd like this to be fixed. It makes bulk storage... bulky.
I've updated the title, as the problem is caused by all mobs, not just animals.
I can't seem to replicate this anymore... Tried chickens in a water pit, flying above rain, and a couple other things which induced the problem previously. Seems like this is fixed! I'm surprised, though... I still get some random fps drops in the nether...