This part of the article talks about what looks like an apology, but really isn’t. If someone seems to be apologizing, but you still feel in your gut that something is off, the explanation might be in this part.
Here’s what the article has to say about when an explanation is substituted for an apology (bolding mine):
Unless the listener is particularly sensitive, an explanation can sound remarkably like an apology. In fact, a relationship between two people is apt to go on a considerable length of time before the party on the receiving end of explanations begins to feel a bothersome absence of genuine contrition in the other. The advantage of the explanation to the person protecting a grandiose self is that it avoids both asking for something (forgiveness) and admitting to a sphere of personal responsibility that includes the risk of inevitable shortcoming. Hence, the illusion of personal needlessness and guiltlessness is maintained. “I would have visited you in the hospital but my schedule got really crazy,” or “I must’ve forgotten your birthday because it came right on the heels of my vacation this year,” or “Your dog just ran in front of my car and I couldn’t stop fast enough” are the kinds of apology-substitutes that may appear to connote remorse, but actually stop short of expressing sorrow and making emotional reparation.”
Legitimate sorrow moves towards repairing and amends. What I experience with him is that while he will express sorrow occasionally, the words lack believability for me because the words aren’t followed by amends and reparation. Instead, in some convoluted way, he begins to feel sorry for himself.
“Evidence that a genuine apology has not been made can be found in the state of mind of the recipient of such commentaries: explanations without apology produce either pained confusion, or understanding without warmth. “
In other words, listen to your gut.