> Are they just flat out missing some infections, or do they require a much higher viral load to indicate positive?

they do require a higher viral load than the pcr test to accurately show infection. the pcr test studies have shown to be 0-30% false negative later in the illness after symptoms have shown (when there are fewer antigens in the body). both the pcr and the rapid tests are expected to have a near 0% false positive rate though with most false positives being lab contamination or mishandling. even if the test is 50% false negative(not the actual number) it would still drastically slow the spread of the virus coupled with other measures. This is more of a defense in depth instead of a firewall; the swiss cheese layers of threat reduction.