Obviously English isn't your first language. When someone says "I'm sorry," or "I apologize," They mean that they regret their previous action, and are admitting it both to themselves and to the people to whom they mistreated. I don't see anywhere in his apology an excuse. It's all apologizing for things he did, feeling remorse, asking us for forgiveness. In some senses, apologies can include an excuse, as is such in the dictionary example you have so kindly given, however, this is not always the case. If PPNL had said ''I'm sorry, but I was stoned as fuck," That would have been an excuse.