I can't tell you the mechanical theory behind any of this, but it's what I have heard. I think this is true for any sort of automatic tranny, torque converter or not.
Yup, same for any transmission with "Park". Due to small amounts of play in the system, when you put it in 'P' on anything other than perfectly flat land, it rolls a little bit and then lands hard on the Park pawl (that's the pin that the OP broke). That puts some stress/shock on the pawl, driveshaft/halfshafts, CV joints, and wheel bearings.
It's not much, but it's worthwhile to just use the parking brake -- not only does the parking brake prevent that little bit of stress, but it also prevents difficulty getting out of Park that happens from so much pressure on the Park pawl, and most importantly it is a much more secure way to park the car. Don't forget, the drive wheels have a differential between them and one can be still while the other one spins, so only one has to be on a slick surface for the whole car to roll if you don't use the parking brake.
OTOH, if you DO use the parking brake, now 3 wheels have to be on slick surfaces (That is, for FWD cars. 2 wheels for RWD).
Once, I put my truck in 'P', got out, started to walk away, and saw it heading downhill with one rear wheel rolling and the other sliding. Ever since then I use the parking brake, or if I'm on a hill / slick surface, I put it in 4WD and set the brake.