There was a 1980 case vs the Pruneyard shopping center in which the Supreme Court ruled that the CA Constitution granted citizens the right to free speech even in private shopping centers. In this particular case, there were UC Students collecting signatures at the mall. I'd be curious to know if you think that ruling would have any bearing on this one should the attorney actually try to bring it to trial? It would seem to me (not a lawyer), that the ruling at least opens the door (a little) for the BB Bail Bonds guys to make a case. I could envision the attorney trying to make a case that since the arena is owned by the city, it should be considered 'quasi-public' (like a shopping mall).
I don't thing the CA Supreme Court ruling in Pruneyard Shopping Center v. Robins - upheld by the SCOTUS would be applicable here.
The CA court held that a shopping center is a public space - "Members of the public are rightfully on Pruneyard's premises because the premises are open to the public during shopping hours" - and recognized the role of shopping centers (as opposed to independent retail establishments) as public spaces.
The HP Pavilion is not a space open to the public - people are permitted under the license terms granted on the ticket.
Since then the CA Supremes have narrowed the scope of Robbins - allowing stand alone Costcos to prohibit public speech and allowing those as part of shopping centers to place reasonable restrictions on the times, locations and frequency of use.
And note that this is an issue of commercial speech, subject to more regulation than private speech - although those differences may be tested in this post Citizens United world.
We may be big and full of cash
but we have rights to spend our stash
Corporations are people too
And so we hope you understand
as we try to buy your land
Corporations are people too
Wacka doo wacka doo