The ground wires in your outlets go back to a service panel. They are all tied together on a strip of metal with set screws. That metal strip is mounted with steel screws to the inside of the service panel. If the inverter is mounted with metal conduit next to the service panel that should enough to bond the two panels, otherwise run a wire from the service panel ground strip to the inverter panel's earth ground.
The inverter panel then gets a copper cable from it's earth ground connection and that goes outside into the earth. The Fluke pdf tells how to make the outside stake/copper cable connection so it will protect the system and you and meet the code.
The hot wires in your outlets all go back to breakers in the service panel and the hot bus bar in the service panel is fed from the hot lead of the inverter.
The neutral wires of your outlets go back to the neutral bus bar of the service panel, which is connected to the neutral lead of the inverter. This neutral bus bar must be isolated from the ground and chassis of the service panel.
The inverter (somewhere upstream of it's internal ground/neutral bond) has current sensors. If current is detected flowing down the ground there must be a fault in the system wiring. The inverter should trip out if that happens. OR, the neutral current and hot current are compared and if they are not equal then there is a leak to ground somewhere and the inverter trips off. If you bond neutral and ground anywhere else, this protection system in the inverter will not work and the inverter should refuse to operate.