No doubt there are some false positives, but that can't be the explanation for all instances of re-infections. Natural immunity is not going to repel the virus like some kind of force field. The question is how does your immune system respond when you get exposed/infected. Maybe the response is so strong and swift that the virus never gains a foothold in your body and you never even knew what happened. Other times, there are enough differences between your initial infection virus and the new one you're exposed to, and you do have an infection of some kind. I think the CDC says they don't know of anyone with subsequent infections because they are intentionally ignoring everything to do with natural immunity.
To me, the smell/taste loss when the sinuses are not clogged up, seems to be a telling sign of Covid. I've never heard of that with a flu. Keep that positive test result. It might not be a bad idea to get another test to reduce the odds of a false positive. Would you say your current infection is less/same/more symptomatic than your first?