And from the Binax (not Binex) sheet we get:
Negative results should be treated as presumptive and confirmation with a molecular assay, if necessary, for patient management, may be performed. Negative results do not rule out SARSCoV-2 infection and should not be used as the sole basis for treatment or patient management decisions, including infection control decisions. Negative results should be considered in the context of a patient’s recent exposures, history and the presence of clinical signs and symptoms consistent with COVID-19. The BinaxNOWTM COVID-19 Ag Card is intended for use by medical professionals or trained operators who are proficient in performing rapid lateral flow tests. BinaxNOWTM COVID-19 Ag Card is only for use under the Food and Drug Administration’s Emergency Use Authorization.
source:
https://www.fda.gov/media/141570/download
And it not accurate to say they are 100% specific as it is clearly indicated that: The BinaxNOWTM COVID-19 Ag Card does not differentiate between SARS-CoV and SARS-CoV2. But it is a good thing because it means it could detect different variant.
Wishful thinking doesn't help with help issue. If you read pages 7 and 8 of the linked document, you will notice, under LIMITATIONS, 15 different situations were the test is limited in its accuracy.
Each one could decide but can not discard known facts to justify his decision.
So those test are useful only when they turn-out positive. They have a much lower significance when the result is negative. Also, if you are positive (with a PCR test) with no symptoms, those test are more likely to give a false negative result.