That is the revised and Parliamentary perspective as put forth in Whig history, a form of scholasticism based upon total opposition to the Stuart dynasty and represented by the wealthy and elitist aristocracy.  It's not "my" POV, it is the international viewpoint.  When referring to the royal dominion of the Stuarts as shown on atlases and maps, they consider it Great Britain because of facts.  You are making a mountain out of a molehill.  Just because the regime changes may have shifted the definition of the United Kingdom since the Jacobean era, doesn't mean that the royal domain was somehow different.  They remained the same lands as inherited by the Stewart and Tudor houses.  Don't let the Whigs confuse you.