Wait a second, why are we blaming the customer when it was Delta people who could not provide the correct information? They called before they left for the airport so they could plan ahead, isn't that what we're always telling them to do?
This.
Delta has done a less-than-stellar job of making it clear (to pax and res. agents alike) that the LAX flight departs from the commuter terminal. If you're not familiar with the setup at SAN, I can understand how it may not be intuitive.
When you check flight/gate status on Delta.com, it says the flight departs from "Gate C3"; no mention of the words "Commuter Terminal". This is all the information the reservations agents have in front of them. If they aren't familiar with the commuter terminal, it's safe to assume that they will pull their airport notes for the Delta SAN station...and, unless that information is updated after this issue, they'll see that Delta flights depart from a normally numbered gate.
Obviously, the lack of station information updates falls on Mother Delta.