I didn't want to call that one out specifically(TACT), because I wasn't sure if that was what people are responding to, or if it was responding to someone else first, but I did have a look over the paper linked to in Nature. That gives citations to 18 other papers regarding HIV positive patients shedding viral COVID.
I did not look at all 18 to be clear, but, I pulled up the first couple and they both refer to PCR testing.