Well, you wrote:
their intentions are admirable.
While their actions may be questionable, their motives are always pure.
This seemed pretty clear to me ;)
Be people overall admire the anti-heroes, because of the feeling of empathy.
This makes more sense in my opinion. It's mainly based on the potential of identification between the ordinary viewer and the displayed actions of the anti-hero. As you said, they are able to relate.
But I still remain with my argument, that I don't think, that's a good idea in general. Severing the connection between actions and intentions to justify the first, can bear heavy consequences.
Thanks for pointing this out, maybe I got lost in the context. I will think about how to clear this out.