Apologizing, when to do it.

I am familiar with the concept that saying "I'm sorry" puts us in the wrong position, and isn't in keeping with alpha behavior.

I recently reread the 16 Commandments of Poon and number 8 stresses that apologizing is almost always not the best option, and that you get (partly jokingly I think) to free "I'm sorry's" for the life of the relationship.

From a practical perspective (I'm playing on hard mode, and I try to be ethical and moral) how can I acknowledge the few times when I WAS wrong, or when I DID really screw something up or anything like unto it?

Thanks.