I always knew it had to be something else besides what I imagined I heard; birds don't shed, they molt. But I always imagined a guy sitting out in the desert all alone with only molting buzzards for company, watching the sun go down...so I sang it anyway.
Later I decided it must be "with the blood that's shed", which made more sense, and it was then that a friend corrected me. I like both my versions, but I like the first one better.