It's good that they're replacing the parts.
What cartridge are you reloading? Looks like maybe a 222 Rem?
My first thought is that you do have to lube the inside of the neck with something. I use Lee paste lube on a Q-tip. As long as the Q-tip has the lube worked into the fibers, a few twists in the neck area is enough.
Also, if the expander ball/die is new or has been cleaned, put a very light coat of lube on the ball itself and the interior of the die before it's used for the first time. The first one is the most likely to stick.
Clean brass is more likely to give you trouble, particularly ultrasonically cleaned or wet tumbled. A bit of carbon in the neck isn't a bad thing, it lubricates the surface so the ball doesn't grab and gall the surface.
If it were me, I'd leave the decapping pin in place. It may support the inside of the rod so it can't collapse, if that's what's happened. If the primer is already out, the pin is just along for the ride anyway, it won't hurt anything.
I'm familiar with the flattened thread crests on the Hornady decapping/expander rods. I think they're designed to slip if something isn't right, like the ball being set too low and hitting the inside of the case. Lee does something similar with the tapered friction bushing that holds the decapper/expander rod.
But, I thought the Hornady ones only had the modified thread on the upper part of the rod where the depth adjustment is? Yours might have been defective.
Finally, be sure you have the height set correctly. On a short case like the 223 or 222 it's critical since there isn't much room in the case to work with. If the ball is too high, it's possible to have the ball in the neck while it's still squeezed down by the die. That's going to be bad news, you'll have compression and expansion trying to happen at the same time.
You should be able to see and feel the case start to come out of the die by at least the length of the neck itself, BEFORE you feel the added resistance of the expander ball pulling back through the neck on the out stroke.
I had to be careful setting up my 223 dies to avoid this situation. In a long case it's rarely a problem, but short cases are a different story.