Neither my RCBS or Lyman dies have this problem, they are made differently. The Lee dies work, but this is one of the features I don't like, and one of the reasons I only use Lee dies as a last resort.
People love Lee dies, because they save a few $ over other brands. For me, its false economy.
I use the Lee hand decapper set, the punch and base (in both sizes) and they are excellent, and virtually unbreakable. The die decapping pin in the picture looks like it would be, as well.
However, as you have discovered, you can pull them out. Lyman and RCBS (and others) use a threaded shaft for their decapper stem, it will not pull out!
I have broken decapping PINS in these brands of dies, but the pins are cheap and designed to be replaceable. Never had one pull out. They do have their own issues, there's no free lunch.
Good luck!