The way currently available COVID-19 testing works is by detection of viral RNA. Since the amount of viral RNA in a patient sample is too low to detect directly, we first need to amplify it by PCR. However, this viral RNA is packaged within all sorts of proteins and lipids that could make it inaccessible to amplification unless they are first purified away. Furthermore, the sample is shipped in "viral transport medium", which is essentially a cocktail of chemicals designed to preserve the virus. Unfortunately, these preservatives often have the side effect of interfering with PCR amplification, so these too need to be purified from the sample.
However, since RNA extraction is usually the most laborious part of the assay, there has been a lot of interest in optimizing the amplification so that it is resilient to all of these impurities. The preprint referenced in our manuscript (https://www.biorxiv.org/content/10.1101/2020.03.20.001008v1) gave us the initial idea that this could be possible, and much of it comes down to the choice of amplification method (e.g. choice of enzymes and buffers) that you choose.
However, even when you choose a "good" enzyme and buffer, you will still suffer an amplification penalty, and this will cause you to return a false-negative on some affected samples because there was so little virus in the sample to begin with. The innovation we have is to spike-in a correspondingly low level of DNA to the reaction mixture. That way, if you see the low level of DNA without seeing any viral signal, you can be assured that the amplification still worked and that there truly is no virus in the sample.