How can you empathize or be sensitive to another person's life if you have no knowledge of their situation. You can
assume that they are in a rotten mood because of that, and by all means you should be aware of possible comments that may touch sensitive to that person.
But to empathize in such the manner you describe, makes them less of a person. They become an object, because its like you've empathy for a less then functional person! And you have no idea if they even care the way that you do about their own arms.
Its akin to pitying the blind. You can be empathetic or be sensitive to the blind person if you've talked to them, but the second you start assuming they are sad that they are blind you have crossed the line, and made them an
object of unreasoning empathy.