When my kids were little and they'd bounce a ball off their brother's head or shove their sister out of their way, I'd make them apologize. Often they'd try to get away with offering up a lame "sorry" without an inkling of remorse so I'd make them do it over and over until I thought it sounded sincere.
How many times do we have to read or hear a politician/athlete/celebrity say something completely stupid/offensive/inappropriate and start with, "If I offended anyone...."? How about, "Since I offended everyone....."? Or "I shot my mouth off without thinking and I feel like a complete jerk." Maybe, "I hope you won't judge me by this insensitive remark because I'm a better person than I just demonstrated."
The latest example would be newly-elected Gov. Robert Bentley (AL) who said only Christians were his brothers and sisters. Maybe he should have spent his first week on the job looking for the cafeteria and bathroom and keeping his hands, feet and objects to himself. A day later he offered up this: "If anyone from other religions felt disenfranchised by the language, I want to say I'm sorry. I'm sorry if I offended anyone in any way."
What the what??? Is there any way but to feel disenfranchised by his statement?
I think that if your remarks landed in most papers and news sites, you offended a healthy amount of people and your spouse/agent/designated toadie should yank you by the arm and tell you to stand up, look into the camera and say you're sorry without blaming anyone for your bad behavior. Responsible parents have been doing that very thing forever.