Yes, that is a big, gaping hole in the story. Multinational companies like Birds Eye, Taco Bell, etc can't back-trace who exactly the supplier was for the meat used in a particular batch of product? It strains credibility.
It’s because horses that live as companion animals or work animals are not tracked individually from birth like cows are. They also get lots of meds during their lives that wouldn’t be allowed in meat animals like cows and pigs. The horses in question are being sold to slaughter when they’re too old to work or ride anymore, and none of them have the sort of history data that meat animals accumulate. In the U.S. horses don’t go into meat but some U.S. horses are sold to Mexico and the meat is shipped to Europe where there -is- a huge market for horsemeat. This is just the tip of the proverbial iceberg on this scandal.