Hi. It is annoying to experience this, but I'm afraid the NZ agent was correct. It was a UA flight that was running late and so up to United to rebook or reroute either from SFO or deal with the consequences in LAX (which would likely mean being put on the UA flight to SYD which departs later, or asking NZ to hold the flight, or putting you up in a hotel overnight so you can fly Air NZ the next day).

Accordingly it is United you need to contact to claim any compensation or reimbursement of expenses.

Hindsight is wonderful, but if it were me I'd have taken the UA offer of seats on the direct SFO-SYD flight and worried about compensation for the downgrade later (and for that dealing with someone more empowered than an airport ticketing desk agent).