I don't know how Morgan talks, but Martin Bashir doesn't sound very American. Indeed, he may sound more British now than he did in England.
But why do Australians speak with a British accent? Their immigration was a little later but not that much, and several generations have elapsed.
They may sound the same to you (and to most Americans), but Britons and Australians recognize that their accents are different. I suspect that we hear the similarities between the two accents but not the differences.
American regional accents are supposed to have similarities to British regional accents of the 17th and 18th century. Over time they've grown apart. Since British and Australian English started to diverge at a later period, it's likely that the similarities would be greater.
Don't ever tell Australians and New Zealanders that they sound alike, though.
In Fawmingten May-en, I understand a version of older English is spoken,
In the dor-yahd.
Jeezily!