This is the "explanation for dummies" from a reddit thread on the study.
Several families had a person test positive, then 8 of the other family members got mild symptoms. When later tested for antibodies, the 8 all tested negative.
There's another immune response that fights viruses (and is different from antibodies) called T cells, and so they developed a test for that that was specific to SARS COV2 and they tested the 8 people and another 10 they were sure had never gotten it. All 10 of the 10 tested negative, so if there is a false positive rate, it is likely low. Then they tested the 8 who had gotten symptoms after their family member was infected, and who had tested negative for antibodies, and 6 of the 8 showed T cells for the virus.
What it could mean is A) the infection rate is somewhat-to-far higher than we thought. Which means the death rate may be lower or far lower than we thought, on par with a very bad flu or 2X as bad, that sort of thing. And B) many more people may already have T cell immunity, potentially some who didn't know they had it, and therefore, they are immune. The 8 who were tested were 69 days out from their symptoms, so we know that T cell immune response will be at least that long. The original people who got SARS 17 years ago still are believed to have immunity.
www.reddit.com/r/COVID19/comments/hdxwf5/intrafamilial_exposure_to_sarscov2_induces/