IMO not true. Photography / cinematography have historically proven to move people enough to take action (eg. war photography, poached animals, rhinos with their horns cut, etc.). Zoos only provides a little more than a photography. Can you pet the animal? Should you if you could? Would that help to make the point of protecting them?
I don't think this justifies transporting the animal on the other side of the planet into unnatural, prison like conditions where they often suffer both mentally and physically.
Sanctuaries are IMO way better in that they are built in animal's natural environment, further from cities, where the animals can live their lives in peace instead of being stressed by thousands of visitors every day.