No. The inverter output protection device (OCPD) does not count towards the sum of the OCPD on the primary supply panel board because that is not what 705.12(D)(2)(3)(a) says. The article is looking at 125% of the inverter output current; not the protection devices. The issue is the potential current applied to the buss of the main panel.
The main panel buss potential is defined as the rating of the service OCPD plus 125% of the inverters output current. That must not exceed 120% of the ampacity of the buss bar. Whatever OCPD are in the panel is irrelevant. If the inverter output plus the main OCPD is over the buss capacity, the way this has been defined allows a reduction in the main OCPD to allow a larger inverter current capacity. The issue then becomes can the new service OCPD support the calculated load for the unit. When the inverter is no longer supplying power, can the main OCPD supply the load?