That looks like a few pieces of ammo I made while learning to reload. That is, if the shell isn't belled correctly (e.g., the case mouth opened just enough to let the bullet in) then the force of seating the bullet will do just that: snag the brass and pull it down on one side.
This could easily happen on an autoloading machine, if the bullet is too big in diameter or the shell mouth isn't opened up enough.
Looks like might be an ammo problem, not a gun problem. Nothing wrong with using cheaper ammo, but might be worth inspecting it before loading.