Hi Wintonian, I think when we've exchanged comments in the past, we have always tried to arrive at the truth. The problem is identified in the wikipedia page for Ulster :
"NI is often referred to as Ulster,[20] despite including only six of Ulster's nine counties. This usage is most common amongst people in Northern Ireland who are unionist,[21] although it is also used by the media throughout the United Kingdom.[22][23] Most Irish nationalists object to the use of Ulster in this context.[21]"
I think that this is probably a fair summary : it is an incorrect term (deliberately and antagonistically) used by unionists. And as the UK is mostly unionist, then the same mistaken terms get absorbed into administrative and media terminology. But all they do is perpetuate an error.
So I mark this puzzle down in that it's not inclusive of the different sections of Ireland.