The trite line "if I have offended anyone, I apologise" is such a crock.
The deliverers of the line have said something that people have objected to so strongly that even the thickhead who uttered the original statement knows that he did the wrong thing.
The apology is worthless when it is subject to such conditions.
A true apology would be along the lines of, "when said x about y, I was wrong, I have hurt the person and I am sorry that I hurt them."
Why does the injured party ask/demand an apology? Easy, because they have been hurt and/or offended.
A certain well-publicised case featured the classic phrase "{lawyer} apologised ''if she suffered any hurt or distress''" - I repeat, if she was not hurt or offended, she would not have pursued the issue through the courts.
Further, it is interesting to note that the perpetrator offered no apology of any description.
An aged sportsman, notorious for attempting to be young by squiring nymphets, showed a disctinct lack of sportsmanship by not accepting the umpire's decision.
Meanwhile, his employers through their tame minions on a current affairs light entertainment show allege he is a good guy by providing a role model. The sports chap has by revealing his prostate condition has apparently encouraged other men to be checked for cancer.
He is a good role model, yeah right! This same buffoon says to ignore his fellow "stars" on his show when they exhibit drunken, violent behaviour because they aren't role models! Hypocrite!!