I've been using a Lee depriming die for a while now on an old, generally worn Hornady/Pacific O7 press. It often hits the web of stouter cases but has yet to shift or bend. I quit cycling the handle after hitting the web, but some cases are just the right thickness that the toggle will still "knuckle over" so the pin has survived numerous maximum leverage events. An especially useful dedicated system now that cases go through an ultrasonic cleaner rather than the old dry media mess.
As for the LC '69 cases, have been using the Dillon swager on 'em since day dot. No dramas. Did bend a .22 calber support rod once, though. My fault as it was grossly maladjusted.