Apparently all you need is to have had one of the several different corona viruses at some time in the past. The tests “may” show you as positive for covid-19.
In other words, the tests “will” show you as positive, because there’s more money to be made that way.
now, people don't typically go for testing without at least some concern that they have at least come into contact, but that's just not my experience with COVID testing.