I send US , Irish and UK citizens to jobs in Australia and NZ several times a year. We stopped doing one-way flights after one was denied boarding in the UK without a return ticket. They all carry company credit cards and cover letters so there was no question about funds. They also have short validity business ETAs for specialist work. It was all down to not having a return ticket.
That may well be, but first you have to get checked in, and that's up to the airline.

Maybe it was "paranoia", maybe not - immigration rules and strictness of their application change all the time - the story you heard last month could already be out of date.