Not only is she over-reacting but she obviously do es not know much about Hepatitis B.
After all, you tested NEGATIVE to HBsAg, so how could she conclude you continue to have Hep B? Highly likely to develop cancer - base on what?
At the very worst, you may have what they call occult Hep B. But this rare and even if you do, the clinical significance is not known. To rule out that possibility, you have to see whether you have hbvdna in your blood. Nowadays, some blood banks will do a nucleic acid test to rule that out.
I heard from the doctor today who seemed quite concerned about my results. I was told that I've had/continue to have hep B and I am not building antibodies so I would likely be considered chronic. She also noted that I would be highly likely to develop cancer. All of this has caught me off guard. I've been referred to a heptologist. I may have spelled that incorrectly.
Is the internal specialist doctor over-reacting???
It looks like you had HBV long ago, that was successfuly resolved and now you also lost HBS antibodies ( 20 years) so you should be revaccinated now. But I would redo the tests in another lab, and test also IgM, antiHBS quant.
The whole issue arises from the fact that you tested positive for HBcAb (everything else is negative). By testing positive to the Hepatitis B Core antibody, it means you have a current or past (but resolved) Hepatitis B infection. But because you tested negative to the HBsAg, we rule out that you have a current infection. So we think you had a past but resolved infection. But as the doctor said, if you had a previous, but resolved Hepatitis B infection, you should have developed immunity, i.e., you should test positive to HBsAb, but your test is negative. But as Rome70 pointed out, if your previous resolved infection was old, you may have lost the HBsAb from your blood (even though the immune memory is there) and that is why he suggested that you may consider getting vaccination to regain that immunity. See point 4 of the explanation from the blood bank.
Finally, I am intrigued by why the specialist is interested in your travel to China, Japan and Israel. China is endemic for Hepatitis B. But Hepatitis B is not transmitted by casual contact, it is by blood to blood contact, by sex and vertically from your mother. So it is not where you have been, but whether you have the risk factors for infection.
To ease your mind, I am sure the specialist will order a repeated test and if he/she is a specialist, he/she will give you the right answer.
BTW, what country do you live in?