" The owner himself could walk around a mall with his dick out and he'd be arrested."

All of this comes from the fact people are in the mall and they aren't being warned and there are a bunch of laws protecting people from hazards in businesses that allow the public to enter.

If the mall owner walked through his mall nude when the mall is closed and it was proven, nothing illegal was done.

If the mall owner puts up a sign "Mall contains nude men and flashers. By entering you agree to be flashed." There is nothing anyone can do, it is his property and he warned them. Usually mall go for the partial protection of "We aren't responsible for our other customers behavior" as to not scare the shit out of people.

The difference is essentially that there has to be a victim for those laws. If the mall owner whips his dick out, but no one presses charges, nothing will happen. BUT the city will not (probably can not, not a lawyer) do it themselves like they could if he was on the road outside.

If it's a private space (EVEN if a "public place") unless there's a specific law against something it CAN be done by the owner.