Interesting. It looks like they've changed their number (for this specific purpose), as all previous texts in my history showed 1300 992 700, but the new texts from today showed 1300771445. I tried calling 1300 992 700 and it has the expected greeting about Qantas Money, but when calling 1300771445 it routes to a generic message not referencing any specific brand, which is also quite suspicious. Incidentally, on both numbers no one answered, and after about 10 minutes holding it hung up on me; great customer service!
Anyway it looks like the root cause of my issues is that in fact my card has been stolen - I found an unauthorised transaction in the online view. So the texts were probably genuine from the thief trying to use the card online. I've locked the card for now and it will try calling them again later.
Edit: Tried again and was on hold for 45 minutes before I gave up, even on the "lost and stolen" option which you would think should be answered quickly. Not impressed with this, Qantas/Citi ...