That's why you keep a record of 1) the positive PPD result 2) the negative CXR and 3) a report from your PCP who can confirm that you are negative for TB.
These three should rule out the necessity of future PPDs and CXRs, unless yah, people are being a pain in the butt/have no idea how TB tests work. Maybe you can request a doctor to do a Quantiferon test on you and you can keep that AND the CXR as evidence?
I worked with refugees, many of whom were vaccinated in their home country or have latent TB and this was how the doctors kept them free of suspicion.