Here in the States, the "a-BERN-ethy" pronuncion appears to have originated in the New England area long ago. I don't know how it may be pronounced in Australia or New Zealand. There is also an American line of Bernethys whom I think were probably originally Abernethys from Northern Ireland. Some of them can now be found in Oregon and Washington States, but the lineage goes back to Pennsylvania pre 1750's. I'm presently hoping to find a living male Bernethy volunteer to confirm this hypothesis via Y-DNA testing.
I think it's clear when one works on the early Scottish lines that the spelling originally had a "e" in the name, corresponding with the Nethy Bridge location in Inverness Shire. However, language does evolve, spelling codifies itself somewhat, pronuciations do change over time, and many Americans now follow the habit of spelling the surname "Abernathy", with the emphasis slightly heavier on the "nathy" portion of the surname.
By the by, Gaelic does not have the letter Y so most of the early Scottish entries typically end in "-ie"
My list of unique spelling variations (mostly from census records) now exceeds 60.
I believe the important thing to keep in mind is Kipling's much cited quote concerning tribal customs, every single one of which is right.
Fighting over the "correct" spelling or pronunciation of the name is about as asinine as domestic spats over whether to have peas or corn for the evening meal.