i think at this point that the only way you will get any compensation is to file a complaint in small claims court in San Jose. Get the name of the manager of the SJC WN station and the names of a couple of top administrative officers of the company. I think you will get a very prompt response once the summons is served on them.

Southwest pulls this stunt periodically and their gate agents use the 10 minute rule as an excuse to get out of paying IDB fees. I have seen it numerous times where I personally know people were at the gate. In many ways Southwest is a really great airline but they have a few odd idiosyncracies, mostly about who boards and who doesn't.