In an example or two of the usage of "my bad" in the links above,

"You just spilled your beer on my term paper!!"
"My bad."

I'm not at all a violent person but I'm not averse to applying a bit of aversion therapy, as in

"You just spilled your beer on my term paper!!"
"My bad."
My fist!

I recall a conversation I overheard in an art class. The teacher was critiquing the work of one of the students, who seemed to take exception to the criticism and said, "Well, gee, Mr. Landberg, I though it was cool."

To which Mr. Landberg responded, "If by 'cool,' you mean 'not so hot,' then I quite agree."

Don Firth