It is incredibly frustrating from my point of view, to be in that situation.
For example, if I ever feel offended by something somebody's done, the feeling of offence immediately vanishes if they can explain to me how I got the wrong idea and how, despite things not going as they'd hoped, they were acting in good faith and with good intentions.
In fact, I tend to assume that people generally act with good intentions anyway, except in special cases. So I'm quite difficult to offend in that respect anyway.
If somebody explained to me that there was no need for me to be upset, because in fact they weren't attacking me or whatever, I can't imagine myself responding by accusing them of making excuses. If I did, and it was pointed out to me that I had, I'd feel ashamed of myself. I'd feel like I acted in a mean spirited, supsicious and graceless way towards somebody who was baring themselves to me in apology.
I guess though, that this stems from my being very willing to question my own perceptions and judgements; I never believed they were infallible in the first place and in approaching the other person with my complaint, I was looking and hoping for an explanation that would enable me to correct my perception and not have to then see that person in a bad light. I prefer to stay on good terms with people if possible.
I understand that some people feel that to be an insult in itself - that is, if somebody seems to be calling on them to question their judgements. Such people tend to be looking more for unreserved apologies and admissions of total fault... it's less uncomfortable for them than a situation that might entail them admitting some fault themselves, be it only unintentional errors in perception. I suppose they also don't mind being on bad terms with others, since they appear to effectively put understanding others and being on good terms on a lower priority level than Being Right.