Just because you perceive to be "paying our wages" confers no right what so ever to be so rude and offensive.
I agree with that, being called an 'idiot' is't pleasant and the OP makes a point of saying he shouldn't have done that.
However, two wrongs do not make a right.
I work in a public facing job (working with middle and senior corporate managers) and before Christmas had some feedback from a customer that I thought was unfair, derogatory and uninformed, a judgment I can make as I am a professional in my field of work and the customer was not (i.e. similar position to a pilot interacting with a passenger.)
Best course of action is to thank them for their input, say you'll check it out (whatever 'it'is) and then either check it out (if they have a point) or ignore it. In my case I chose the latter course of (in)action.
If the pilot had done that, the OP would have been reassured and probably telling his friends what a good airline he flew on. In my case, I got a message from the company I was working with thanking me for the good job I had done and offering me a couple more engagements.
Sh*t happens, we have to get on with it, especially in a recession, where customers are thin on the ground.
Obviously, if someone is threatening, then that is a different matter.
Also, it sounds as if the LAX security people did a pretty good job of mediation.