So we still don't really know if Tania is immune. If this person was a slow turner, would there have been enough of 'whatever makes people turn' in the bite to make Tania turn? Could it be that she is turning even slower? We don't know of any other person who had time to clean the wound after being bitten.
The same with Saul, we don't know it there would have been enough active 'whatever it is that makes people turn' on the bullet that went into him. It could still be just the antibiotics that made him able to breath when he went to ground zero.
It could be a coincidence that they both have immune seeming happenings.
Just playing the Devils Advocate.