Yeah, I can understand such misconceptions.My friend and I were mistaken for Australians in Kentucky, Tennessee and Georgia back on a tour of the western battlefields in the early 90's, not long after Paul Hogan became a big thing in the USA with his Crocodile Dundee movies and Talk Show appearances. We both had strong London accents at the time, though not Cockneys in the strict sense of the word.
( Steve Irwin and the Outback restaurant commercials didn't help matters)
Personally I love an Aussie accent !
I'm actually mesmerized, and could listen to their accent all day.
Recently, I've been watching a few Aussie & Kiwi You Tube channels.
From the voices I've heard, average Australians do sound different from average New Zealanders.
Kind of like us.
Example: we are all from the Southern USA, but a Virginia dialect is nothing like Georgia, Mississippi, Alabama, Tennessee or Texas.
But I am very much aware that accents within the UK ( especially England ) are vastly different among regions.
I've always enjoyed the variations within our language.