Does apologizing entail recognizing being at fault?

Consider this example:

I'm sorry if you got the impression that I meant to insult you. That was not my intention.

Would it be correct to say that the above person apologized?

All the dictionaries I have checked defined "to apologize" as admitting one's fault. However, in the above example, the person is not conceding he is making a mistake; he is merely clarifying his intent and, well, apologizing if he hurt the other person's feelings. Yet, based on my understanding of the verb, it would be adequate to say that the person apologized.

So, does apologizing really require being at fault?

Solution 1:

This topic was addressed by The Idealistic Pragmatist back in a 2005 blog article:

Way back in the year of this idealistic pragmatist's birth, Searle laid out the criteria a statement has to fulfill in order to qualify as an apology, and in layman's terms, we can say that it requires two parts: 1) regret (the "I'm sorry" or "I apologize" part), and 2) responsibility (some explicit statement that you were the one who did the thing that's being apologized for). The statement "I'm sorry that I borrowed your jacket without asking," for example, meets both of those criteria.

She dubs the type of sentence you cited above as a "fauxpology", where an ersatz apology expresses regret but not responsibility:

Often, people will use a rhetorical trick in which they make a statement that has a lot of the superficial trappings of an apology, but without one or both of those basic criteria of form. I call these statements "fauxpologies." ... Another classic type of fauxpology is to say something like: "I'm sorry if I borrowed your jacket without asking." The responsibility criterion is similarly missing here, since the speaker is expressing regret only if a condition is true, but weaseling out of any admission that it is true. The effect of statements like these, if used skillfully, is to make recipients feel as if they should feel apologized to, despite the fact that no actual apology ever took place. They're not apologies, but rhetorical tricks for weaseling out of taking actual responsibility.

Solution 2:

The statement

I'm sorry if you got the impression that I meant to insult you. That was not my intention.

is an apology of sorts, but it borders on the confrontational. By saying "you got the impression" you are absolving your own communication of any fault, when in fact there is a chance you may have phrased your statement in a way that could be misconstrued by well-meaning people.

If you are really concerned that you have offended someone, it doesn't hurt to admit that possibility with something like

I'm sorry, perhaps I didn't make my meaning clear. It was not my intention to insult you.

This assumes some responsibility for the missed communication without losing your own dignity.