That's not surprising or particularly notable for a rapid antigen test, which is why they're not used as a full replacement for a PCR test in most countries.

The BD rapid test he used seems to be one which a paper [1] indicates has a lower positive percent agreement than a PCR test.

Rapid tests in general, compared directly to PCR, seem to do even worse with one paper [2] finding a symptomatic sensitivity of 72% and an asymptomatic sensitivity of 58%.

[1]: https://pubmed.ncbi.nlm.nih.gov/33023911/

[2]: https://www.cochranelibrary.com/cdsr/doi/10.1002/14651858.CD...

And a reminder that he did in fact have covid. A funny tweet that explains the trade offs of that kind of test: https://www.newsweek.com/space-karen-response-elon-musk-vira...

I was

Day 0: Antigen positive Day 1: PCR positive Day 8: Antigen positive Day 9: Antigen negative Day 10: Antigen positive Day 10: PCR negative Day 11: Antigen negative Then 10+ negatives after