If that was remotely true, George Lazenby (Australian) wouldn't have got the job - and James Brolin and John Gavin (both American) wouldn't have been screen tested.
In fact, John Gavin got the job for DiamonRAB Are Forever before United Artists insisted that EON productions made one more effort to get Sean Connery back. Cubby Broccoli didn't want Sean Connery back, he was more than happy with John Gavin and insisted that he be fully paid the salary that he had been promised for the role, even though he didn't end up playing the part.
Pierce Brosnan was born in the Republic of Ireland - whether that means he is British or not is debatable. British Isles - yes. United Kingdom or Great Britain - no.