Once you have a successful PCR, you have billions of copies of your target sequence that are easy to aerosolize and/or transfer by contact onto your pipettes, gloves, and other lab surfaces. When a few of these molecules find their way into a new PCR you just set up, you get a false positive. There are protocols clinical labs employ to avoid this (e.g. never open the cycled PCRs in same room where you set up new PCRs, etc.) but they require strict adherence. (Or you can just give up all your sensitivity and only detect the cases with a huge viral load.)

Looking at the assay - it uses a dual labelled probe. That gives the specificity in addition to the PCR primers. Primers themselves presumably aren't selective enough.