Picking up drops while inventory is full destroys the dropped item

I was in a survival world, and a zombie had picked up one of my items. My inventory was completely full (I wasn't aware of this), so I killed the zombie. I heard the sound effect for picking up a dropped item, but when I checked my inventory the item wasn't there.

I also re-created the situation in my creative world, you can watch a video of what happens, here: http://www.youtube.com/watch?v=znq2suSwJ80&feature=youtu.be

As you'll see, the zombie DOES drop flesh, but I don't get the item even though it appears that I do.