Believe me, when anyone says any of those phrases, you can be sure they REALLY do care, and to them its a big deal. This is just a backhanded way of taking the wind out of your sails, instead of trying to make a case of their own.
the worst one ever is when someone says to you “no offense” after saying something offensive. like ” your hair looks gross today” “but no offense!” like what was that if not offensive?? i absolutely hate that and i never say it.