Covid suspicions. False positives?

I’m not a conspiracy theorist, I’m double vaxxed, I believe this is all real. But something happened recently that had made me very confused and suspicious.

My brother in law is the safest person I’ve ever witnessed during the pandemic. He has asthma and is overweight so he’s very worried about covid. He wears 2 masks to work, a face shield and gloves, does curb side pick up, doesn’t visit with anyone. But lives with his parents.

He was apparently gardening one day and stood up wrong and smashed his head on something. He had a headache after so his mom said he should go to the hospital to make sure it wasn’t a concussion. Because headaches are a symptom of covid, they made him get a test and it came back positive. My in laws decided to get tests too because they live in the same house and they tested negative! No one knows how he possibly could have gotten it and he feels no symptoms at all other than his headache from bumping his head.

Could he have gotten a false positive? Anyone know someone who got a false positive?