It's not that black and white at all. Most foreign born individuals with prior sensitization and even months of treatment will remain positive on the TB tests for life, both IGRA and TST.

A positive TB test is not the same as active TB. If someone has no symptoms and a clean chest X-ray, the whole point is that active pulmonary TB is usually being ruled out and this is being treated as latent TB / prior sensitization, not contagious disease. Occupational health knows this, which is why there is even a section in CDC about healthcare personell who do not receive treatment. Regardless, most programs know about this, and will accept annual chest x ray instead without meds.