One important point is that the current 20th Edition of API 6A is also ISO 10423:2009 (Modified). That 'modified' is important because differences between API 6A and ISO 10423 are not identified in the body of the spec. Instead, if you are working to API 6A, you must apply all changes that are detailed in Annex O. Note also that Annex O is updated with each release of new addenda and errata; so far, there have been Errata 1, 2, 3, 4, and 5 as well as Addenda 1, 2, and 3, so you must make sure you're using the latest Annex O.
That said, yes, subclause 4.3.4 (Closure Bolting) states, "Bolting stresses, based on the root area of the thread, shall not exceed the limit given in Equation (9):"
But Annex O instructs us to replace the above with, "Bolting stresses, based on the minimum cross-sectional area of the bolting, shall not exceed the limit given in Equation (9):"
So no, the root area is not necessarily the design requirement.