i dont know.
however here are some of my thoughts.
-depends on the intentions. if the intention is genuine then its easy to accept. if you cant tell what their intention are - do they really mean it - its so much harder.
i feel one of the worst things the British has taught us after bread and butter is 'i'm sorry. oh i shot the gun and accidently killed your son, i am sorry.
for me - after all these years - lookign at life and trying to live better this is what i have come to the conclusion.
what matters is what "i" say. which means have the courage to speak your truth. so i mostly, if i have the courage, speak the truth. saying please give me a few days to understand what you are saying. you just apologized for <something this big> i dont know how to fathom that. so i am neither accepting or denying your apology - but for sure right now i dont know how to respond to you.
i have found - every. single. time - EVERY SINGLE TIME - i speak genuinely its well taken. UNLESS the person is messed up and not able to 'hear' me. then it was my bad judgement to speak up. HOWEVER sometimes its sooooooo freeing just to say your words whether they were heard or not.
so there is so many layers to it.
however when someone has done something very very big - its sooooo hard to say i'm sorry. it goes beyond sorry. so i tend to see it as someone wanting to make amends. THAT is key. not what words they use. i knew how sorry my ex was that he couldnt stay in the marriage. that he wanted out. but it still hurt and i still became single. but somewhere there was within me - through all the pain - some peace that he got it - before it got hidden under a lot of unpleasantness.
i am lucky i have dd to work on. that she is open to who i am and what i say. so when she says sorry - sometimes i am so not ready to hear it. it doesnt change the fact that i still stubbed my toe and it hurts so bad due to her. once i have had my composure back i tell her hey i know you are sorry. no one does these things purposely. but gosh darn it STILL hurt. i know you really want me to know how sorry you are. its ok. i understand.