I am well aware of the difference between IgM and IgG.
I think the data matches with what we all expect. You can dive into the specifics of their assays and that might answer your question The real problem has been false negatives which are running 20-30% not false positives. You could ask for the cross reaction studies later but I think it is important people understand this illness is far more prevalent than most think.
I figure an MD knows something about the different classes of antibodies, and the activation profiles for each type. But the average reader might not, so I added a short description of each type.
Yes, there are false negatives which have a different mechanism than false positives.
This paper (not peer-reviewed and published by the same publisher as the Stanford paper that everyone is going on about) discusses both false negatives and false positives. The authors suggest that the definitive diagnosis of Covid-19 should depend on two different assays: rtPCR to detect viral RNA, and serological testing to detect total antibody, IgG, and IgM. I found this statement of particular interest: "The specificity of the assays for Ab, IgM and IgG was determined as 99.1% (211/213), 98.6% (210/213) and 99.0% (195/197) by testing of samples collected from healthy individuals before the outbreak of SARS-CoV-2." (Last sentence in the Antibody measurement section.) That suggests that there is at least a 1.4% error in antibody studies--which is very close to the rate of Covid-19 seroconversion the authors of the Stanford paper claimed to have found in a (biased) sample of non Covid-19 cases. In other words, the finding that there was a 1.5% seroconversion rate, inexplicably "corrected" to 2.49%/2.75%/4.16% using different models, is well within the margin of error of the immunoassay.
While I certainly accept that there are presymptomatic cases, I am less convinced of asymptomatic cases, especially when the models and estimates propose a prevalence that makes Covid-19 more infectious than any known respiratory virus. Whenever someone makes such a hypothetical claim, you have to weigh it against the body of knowledge within that field to determine whether it is biologically feasible. Is it plausible for any virus, even an airborne virus (which coronaviruses are not), to have an R naught up in the 50 or higher range?