The situation in the drama was much more complicated. As soon as everyone in the hospital found out there were an AIDS patient among them, every patient left and no surgeon and nurse are willing to volunteer for the operation beside two male and female surgeons. I mean the situation was awful and I can't describe it well. And guess what? As soon as main artery that had been squeezed were uncovered, blood suddenly squirted into the surgeon's face. And i don't know what happened after that.
BTW, some of you guys caught some odds that i didn't. It was unprofessional that the surgeons were not properly equipped. It's just drama and some twist must happen.
In this specific scenario:
Despite popular belief, HIV is not a very infectious virus. Even if you accidentally stick yourself with a needle that was used on a patient with AIDS, you have a very small chance [1/300] of being infected. (Hepatitis B, however, is a whole different story.) Getting splashed with HIV infected blood (unless you have oozing, open sores on your skin) is an even smaller risk. In real life, if there was any accidental exposure to HIV infected blood, taking a massive dose of anti-retroviral drugs will help prevent the virus from replicating before it can spread all over your body and go into hiding. It's not as big a deal as you're making it out to be.
In general:
If you're firmly convinced that your life is endangered by treating a patient, you don't have to do it. If you know that intervention wouldn't help the patient, then you don't have to help. This is why the Red Cross and the UN don't set up shelters in the middle of war zones.
But, personally, if I thought that I could save the patient and the chance of saving the patient was higher then the chance that I'd be infected with HIV, then, sure, I'd do it.
Moral of the story:
Get your Hep B vaccines! Hep B is much more infectious that HIV, and although Hep B usually isn't chronic, you don't want to run that risk.