I want to use Eddard to cancel Parmen's save on Robert Baratheon, but I wasn't sure if the save effect was considered to have chosen him

To provide a little more detail, since that was posted from my phone in hopes of a quick response, I was playing a melee and my friend defended a deadly challenge with Robert Baratheon with knighted and a few other knights on a You Swore an Oath turn, because my brother attacked him forgetting about the plot. The Baratheon player had Ser Parmen Crane down along with plenty of influence (but no dupes on Robert), so he defended and got a bunch of renown without having to kneel the characters, then he chose Robert to die to deadly and knelt an influence to save him.

Now, where I'm a little unclear is what constitutes an effect "choosing" a character, because I had Eddard Stark out and could have potentially cancelled that save (if it meets the criteria) to kill off Robert and cause him the loss (I would have won it had he not then been able to attack with those same renown characters and get 2 more power on Robert, on top of the others - not to mention the fact that he would have lost the 4 already on Robert).

So, again, in case that's all TL;DR, does a save effect choose the character that it's saving? Apologies for the brevity of the previous post.

The answer in your situation is NO. The saved granted by Parmen does not include the word "choose" in its text (nor does any other save that I know of) and that is the only criterion for choosing.