The dispute down under that landed Apple (AAPL) in an Australian federal court Tuesday is a bit more complicated than initial reports suggested.

According to the Sydney Morning Herald‘s Lucy Battersby, the Australian Competition and Consumer Commission (ACC) contacted Apple on March 15 — the day before the new iPad went on sale — expressing concern about the name of the product.

Apple’s marketing material describes the higher-end iPads sold in Australia as “Wi-Fi + 4G” even though the devices can’t connect to Australia’s 4G networks. (There are two commercial 4G standards. Australia adopted the Mobile WiMAX 4G standard. The U.S. and Canada went with LTE. UPDATE: The Morning Herald didn’t have that quite right; Telstra, an Australian carrier, supports LTE, but at a different frequency than the one Apple uses. See here.)

According to Battersby, the agency wrote to Apple again on March 20 and March 23.

“On [March] 26th in a telephone call,” she reports, “Apple agreed that it would publish some corrective advertising and offer refunds to everyone who bought the iPad and e-mail everyone who bought it, and tell them that it is not compatible with Australia’s 4G networks. However, there was some disagreement over the wording of the correction, and the two parties ended up in court with the agency today alleging that Apple mislead consumers.”

Battersby didn’t specify exactly what words the two sides disagreed about, but we can guess.

Apple uses “Wi-Fi + 4G” in its marketing material worldwide. Knowing how much value the company places keeping the language it uses to communicate with customers simple, clear and consistent, we suspect it would rather give back every iPad sold in Australia than change that language.

We also suspect, knowing how much Australians like their Apple products, that the company’s offer to give back their money won’t get many takers.