Essentially, yes. I'd be a mite ticked off if I was LA, too. LA flies AKL-SCL and LAX-SCL, and could easily take feed from CX at both places if both airlines wanted to coordinate better. You're dumping a bunch of capacity on a partner's route and potentially depressing prices if you can't consistently fill two planes on a route like that, and hosing your alliance partner (and it's not like CX is making record profits these days either). Is there any evidence that those North America/Oceania-South America routes are underserved and could use an extra 77W worth of seats every day?

The whole point of alliances is to put your customers in hubs/logical connection points for other partners and let THEM handle the "last mile"- it lets you concentrate on what you are good at (in CX's case, serving Asia), lets them do what they are good at (serving the Americas). Using a very expensive longhaul aircraft to essentially duplicate existing alliance service is a poor use of valuable assets.