I don't think they are supposed to accept 'downers', but some do anyway.
The vast majority of downers are just that - can't walk. Old, broken leg, etc. I can't imagine a house taking a cow that's foaming at the mouth or otherwise suffering from a disease.
They test for this by checking it's reflexes.
Can errors be made? Well, we just learned that they can. Did the industry get a wake up call from hell? You betcha. I think it would be a massive competitive advantage to "sell safety" by earning credibility with the public.
Remember how Intel recalled all early Pentium chips even though there was a virtually no chance of the error affecting anybody? It wasn't about chips - but rather trust and integrity. Andy Grove, Intel's CEO at the time, called this, a "Strategic Inflection Point". It probably saved the company and neutralized a whole squadron of trial lawyers that were fixing to feast on Intel's misfortune.
I'm not expecting the beef industry to recall every beef product, but they need to do a little more than just the government minimums. And then they need to communicate how well they do their job to the public. After all, lose their trust and you're outta business. As it stands, they're going to lose a bunch.
I, on the other hand, will enjoy a respite from record prices as a beef consumer.