PCOS can give false positives
As for further up the thread talking about a BFP at 4DPO.... trip down the Fallopian tubes after fertilization takes 3-6 days, implantation takes 1-7 days. Starting amount of hCG is usually 5 but can be as low as 1.
So if someone has their eggy take a 3 day trip, it is able to implant immediately, they have 5miu of hCG to start with and it doubles every 48 hrs or less.... very early BFP!