This is Texas. No permit or license required for any long gun, loaded or unloaded, in public or private, concealed or carried openly. Why in the trunk, though? Who knows.
Just seemed a little weird. Women I know all have CHL and their gun is never far from them. Seems like having it in the trunk of your car serves little good - although it worked out okay for her.
Like you said, who knows! It is Houston, after all.