You are confusing sensitivity with empathy. I can assure you that the victim of a BPD relationship does not think of his SO as empathetic.
They may think of themselves as such with others but with their SO, they are a Gorgon.
They do not exercise the restraint that almost everyone must. Empathy is not an excuse and a poor one if it used.
Empathy is a psychological defense mechanism used by those with BPD to justify their otherwise malignant and inappropriate behavior.
That and Denial are the most common defenses that those with BPD use. If they accepted even a part of their malady, they would have some hope.
The biggest impediment to their recovery is Denial.
And it is a shame.