The word "wrongfully" is subjective. Most of the time people give an insincere apology, they feel they are not in the wrong (i.e. their action was justified in some way).
If I believe my action was actually wrong, I can't think of a situation where I would give an insincere apology.
I think we all give insincere apologies far more than you suggest. Just this morning I told a recruiter "I am sorry for not getting back to you earlier". It was social lubricant... some polite formula as part of a purely business relationship. I am not actually remosefull.
I will apologize on the bus when some jerk cuts in front of me an I bump into him. Again, I have no remorse, what I am really saying is that we bumped and I don't want any conflict.
I think insincere apologies are common practice in funcioning adults.