An apology that has been insisted upon, imposed, or coerced, is NOT the same as one generated from a contrite heart. Amirite?
Do we really and truly believe the apology of a politician or famous person who gets caught up saying or doing something completely outrageous? Most of these people only apologize (if they apologize at all) because of the attention it creates in the media or pressure put on them by some activist group that was "offended."
Contrast this with someone who personally does something towards you and then realizes on their own how badly it hurt. If they come and apologize and tell you they want to make things right, that means a whole lot more.