Somewhere between the stomach and the anus fecal matter is created. E. Coli lives along the entire tract. You're not wrong, but it's not just fecal matter which contains E. Coli. Basically the entire process involves it. Stating that shit on your meat is the source of E. Coli is understating the issue but it also triggers a more visceral reaction.
The stuff which causes you to have diarrhea that gets on the news is caused by the contents of the digestive tract being spread over your meat. Whether it's technically fecal matter or not doesn't really matter if it's stuff that will cause YOU to lose control of our bowels.
Proper butchering SHOULDN'T spread the contents of the digestive tract on the large muscles.
This way undersells what's actually happening: fecal matter from the intestines gets onto your meat. This shouldn't happen with proper practices.