Especially since cows are, you know, herbivorous. Organic does NOT mean grass fed by the way. They may have been grass fed, heck any cow may have been at least partially grass fed.......
The ONLY way to know is to contact the manufacturer of whatever it is you want to buy, and ask them.
Then hope they don't lie to you.
Dead cows as feed? Never in my days have I heard of that. Especially since cows are, you know, herbivorous. Organic does NOT mean grass fed by the way. They "may" have been grass fed, heck any cow "may" have been at least partially grass fed. It means that they have only eaten organic feed (i.e. grass, organic hay, organic corn feed, organic anhydrous, etc.). And It means that they have never had growth hormones or penecillin.
Organic beef is, well a money scheme. Eating normal beef is JUST as healthy and nutritious as organic/natural (natural beef is a middle man between organic and normal beef it simply means the cow was drug free) but unlike org/nat beef, normal beef is not outlandishly priced.
As for Lean Finely Textured Beef (or as the media calls it....pink...slime) The ammonia is so trace that scientists say there could never be a possible health problem linked to the product. Just like coca-cola. It has trace amounts of cocaine in it, but it's so insignificant that there could never ever be anything bad about it.
In short-Don't fall into the media trap that only organic food is edible. It's all about money.
