I had a TB test when I was 8-10 (can't recall exactly) and tested positive, which basically means at some point I have been exposed to TB, but I do not have it. So, any time I need a TB test now, they just go straight to x-ray, as the regular test will always show a positive result.
The point: if doctors are hesitant about giving the full-on test, see if they will do the x-ray for it instead.