I believe there was an Alaska Airlines fare from PDX-PSP for $0 a while back... can't find info in search, but maybe someone knows how to search archives.

From what I remember, as a casual follower of the story, is that AS at first wanted to charge people some kind of "reduced" fare when they checked in, saying tickets weren't valid, but I think in the end they honored the fare.

The famous $0 Hilton Mexico City rate was resolved by granting people their first night free, then charging for remaining nights that people may have booked.

So, my hunch is that if the airline issues the ticket (electronic or paper) with a ticket number, they are bound to honor the ticket at the $0 fare.

Regarding taxes, most likely taxes will be piled on top of the $0 base fare.