I've installed dozens (or maybe even hundreds of chains), either with a cheap chain tool or the Park mini, and I've managed to damage a few plates with with either tool. I have never broken a pin on any tool however. (Knock on wood).
Also, I always drape the chain on the BB shell when I'm removing or installing a chain to keep tension off it.
I never remove a chain link pin completely, not even on the few offal links at the end of a new chain.
I never use connector links because I have never encountered on on any chain.
So based on all this, and what I've read here already, I have to concede that
the problem is me 
, not the chain, and not the tool. I'll try to be more attentive in the future.
FBinNY, and Bradtx --- I understand that the references to "peened over" rivets and caveats about not reinstalling them is germane to modern (7 or 8-speed) chains only. (If so, it's a non issue for me, since I don't work on any newer bikes.)
Thanks to all for your insights! I can always count on getting the straight story from the Bike Mechanics!