One thing I've also heard about "crude protein" sources, and this could be urban legend, is that they're not too picky about what constitutes "protein". For instance, say a turkey or chicken has a huge benign (or even malignant) tumor in its body-- that tumor ends up included in the protein source. Pretty ick, and possibly even dangerous, if you ask me.
Well, I don't know if they'd go to the trouble to single out the tumor, but "animal byproducts" is everything that's left when the good stuff's been taken. Including the yucky bits.
Not that there's anything inherently wrong with that, really. Some of it is undoubtedly of good use.
I simply reject any pet food that lists unidentified 'animals' in it's ingredients because this is codeword for the less than appetizing product of both horse slaughter, and animal disposal (including euthanized pets) that end up at rendering plants.
If the label ingredients say "Beef" or "Chicken" or "Lamb", or "Beef byproducts" that's what it is. If it says "Animal"... well...