I am having trouble with this. Implies to me that the person making the statement does not feel it. I don't believe we can know what others feel, they have to tell us and I see no point in my saying to you, "I cannot tell you how sorry I am that this happened" if I am not. I would say such a thing so you know where I am in relation to you and your life/situation, to acknowledge that I am listening.

My feelings are mine and anything that arises from you as a result of my expressing myself is yours. The words are not as important as the relationship. If a child says, "I hate you!" and "means" it to his mother, that is probably perceived differently by her than if a teenager says it or a spouse/lover or friend says it. If I expressed my empathy here to you as a result of something you wrote, your response would be different than if your T expressed empathy as a result of something you said in therapy but your perception would be all yours, not a result of the other person's expression of their empathy.