I don't KNOW how it goes with cattle, but human testing can result in false positives, so, LOGIC tells me it can happen with other 'critters'. Of course, authorities must be diligent in tracking down even the most remote possibility of a real problem.
Our local school used to use volunteer labor to help prepare and serve a hot dinner at school....the 'labor pool' was the mothers of the students, of course. I was one of them at some point between 1966 and 1983, the years we had kids attending Midland School. We were required to have TB tests, annually I believe. One year I tested positive. No other indication was found that I was a carrier. I did share with the medical people involved that when I was about six years old, I had an elderly grand-uncle who had been treated for TB. He apparently was 'cleared' by the powers that be at Sanator, SD (a special medical facility for folks with TB) to live at home with no restrictions. Because he and his wife were my favorite people, I was allowed to spend quite a bit of time with them during his last years. Some of the medical folks agreed with me that I could have somehow acquired antibodies which caused me to test positive for TB, tho I did not actually have it. I did continue working at school and no one else ever tested positive. I do think it somewhat strange that I was simply told to not have the test anymore!
Anyway, I do wish the best to those ranchers who are having to deal with all the extra work and the usual costs involved, to get their herds cleared as being safe for commerce. Most likely there was absolutely no fault of theirs, yet however small the effort needed, there will be costs to them that are not re-imbursed.