The terminology is regional. In some places they call them jacks, and the same things are called liners somewhere else.
The 2x4s or whatever's used to make the rough opening would be called the door framing, not the door frame. I've never heard the rough opening for a window called a window frame.
The jambs and trim/brick molding make up the frame.
^^^This. Think of a picture frame. The "frame" is made up of components that hold the picture. It is not the wall you hang it on. Difference between a door frame and door framing. The door frame holds the door, while the framing holds the door frame. According to Merriam-Webster.....
Definition of doorframe:
the jambs and upper transverse member enclosing the sides and top of a doorway and usually supporting a door
Door frames can be pretty flimsy, kinda the reason for deadbolt locks with the heavy #12-14 screws holding the strike, long enough to reach to the framing. Not just those little 3/4 inchers screwed into the particle board jamb. Also why, in areas where folks don't use storm/screen doors, they should consider outswinging exterior doors. Much harder to "kick' in.
Could be regional too, I suppose as are many building terms, but been a carpenter specializing in trim and cabinetry for 45 years, and never called the rough opening for any door or window the "frame". Lots of folks call those skinny things under their handrail "spindles" too.
That said, very few folks that hear a story told, second or third party, is getting the truth, the whole truth and nuttin' but the truth....so help me God. Gonna be some embellishment and some "slight adjustments" to the facts. Just human nature.
I don't doubt the story at all, but folks remember things slightly different than they actually happen, and a good story gets better everytime it's told. Scientific fact.