the primer crimp is usually one of two types, either a "ring" or a "stab". US ammo makers generally use the ring style, foreign makers often either type.
Both are done the same way, the primed case is "bunted" (struck) by a tool that displaces a small amount of brass from the UPPER EDGE of the primer pocket. This is NOT a critical area.
It is done to meet military requirements to keep the primer in the pocket no matter what.
The crimp varies in size, depending on what round, who made, and when. Most are quite visible, some are not so easily recognized.
Are Lake City cases considered "crimped" in the "military brass" sense? I know I can't re-prime them unless I take my chamfer tool and break the edge of the pocket; but I don't know if that is actually what is usually called a "crimp."
Lake City is a govt arsenal (staffed mostly by civilian contractor workers) and they produce ammo to the mil specs, which means crimped primer pockets.
If you have to chamfer the lip of the pocket in order to seat a new primer, what you are doing is cutting away the brass that forms the crimp. Some folks prefer to swage (push) the crimp out of the way, and generally swaging also allows you to "uniform" the entire primer pocket. Chamfering (cutting) only cuts the top edge of the primer pocket, removing the crimp and not affecting the other dimensions of the primer pocket in any way.
I"ve done both, chamfering works fine for me, quick, simple, easy, and doesn't take a special tool that only does one job like swaging the pocket.