The problem is if the airport staff view this transaction differently from the folks at LAX. It's entirely possible -- either because they've been told different things, they have a different attitude, they're more observant, they had a bad hair day, whatever. When you've paid zero, I think you are NEVER completely safe until you have returned home (and even then you could be sued for something like theft of services, but that seems extremely unlikely). It just takes one computer message, or one suspicious airport agent, to completely ruin your day. And your bargaining position isn't very good when you're at the airport trying to board a flight and the agent won't let you.
Again, I hope everyone's tickets are honored and everyone has a smooth and peaceful airport experience. But given the nature of this situation, that seems like only a possibility, not a probability. In other words, don't count on it and be prepared for anything.