Thanks to all for the responses. And thanks for pointing out the breaker before inverter issue. I do indeed have the shore power going to a main breaker then to the inverter. So my mistake for saying in original post it was 'direct' from shore power to inverter.
With that, my concern is still that hot and neutral go to inverter together while the ground goes to the AC ground bus. I too thought that all three would go to the inverter together and then out together. Not at the boat
at the moment but I will check to see if there is a ground from AC bus to inverter then it is all settled. Thanks again for the help.