That is the way it is wired, shore power go's through the inverter and inturn the inverter fan runs all the time and is noisy.
I moved my inverter to the floor and built a sound deading box over it leaving the front and back open for air flow.
Here is a pick in the stock location. I did not take any pics after I moved it but I could if needed.
The green wire is the trailer feed from the inverter and the purple is the AC feed to inverter.