The doubt is sometimes valid, as it might not seem (or in fact be) reasonable for the offended party to be offended. If person A says something that person B takes offense at, but person A had no intention of being offensive, _and_ it is not obvious (or rational) why B is offended, then it makes sense to offer "if what I said offended you, I apologize". That's polite and considerate.
For me, it's the least acceptable level, it's lowest common denominator least-worst choice. In public life, it has become the first choice goto form. I believe its driven by two forces: lawyer and insurance company "never concede" drives, which are at best asocial, and an underlying belief on the part of the apologist they did no wrong.
If an apology is genuine, heartfelt, it requires no qualifications. If it is qualified something is not reconciled.
I agree that in hypothesis, an issue could be moot or open, but do you really think this predominates?
I am by the way a serial offender and a serial apologiser. I know from bitter experience how hard it can be to accept fault and apologise for hurt caused.
