I am sorry to hear you had to go through that. Here are some facts about the computer system, employees, and booking system. If the agent lied, then that is not right.
Maybe the agent's computer said their were no available seats on Delta. Their have been times the computer will tell me that their are 5 seats left on Continental and I will book it only to find out that their are really no seats left. The problem with that is, once I move the ticket to another airline, the other airline are the ones who have "control" of that ticket. Their is nothing I can do for that passenger at that point. It sucks I know.
In order for an agent to "move" your ticket to another airline many complicated program entries are required and if the agent has little or no experience with a certain type of ticket, then the algorithm is missing an exponent to the formula. Many of us are not given the training to identify or recognize how to find the missing characters to make the ticket change. We are put into the front line to learn the hard way. It sucks I know.
Maybe the agent did not lie to you. I don't know. But I suggest you make your complaint formal. Perhaps that will help us all in the long run.
www.aa.com/customerrelations
Be sure to include all the facts. Flight numbers, dates, etc. Good luck to you.