An apology is merely an admission of inappropriate behavior and an implied verbal or written contract to cease any such future behavior. It should never be considered as else.
A wrong committed is and will be an ongoing victimization until such time as an apology is made by the perpetrator, a penance offered by same or a moderator, accepted by the victim and carried out to the satisfaction of all parties involved.
The concept of letting bygones be bygones can only be appropriately offered by the victim.
Let's all be honorable by being fully responsible for our actions and their consequences.
I would further suggest that "I'm sorry, but"s are not, and should not be considered sincere apologies.