I like your take, you said it better than I did.

I disagree. Lawful or Chaotic describes ones adherence to rules; either those of society or their own moral code. Chaotic would describe one who does not adhere to any rules or guidelines; nothing is off limits except that which would violate their alignment on the Good-Evil axis. Neutral would mean that one would bend those rules to achieve a particular outcome. Lawful is going to stick to the book; they're very conservative.