Is this a charger/inverter or just a straight inverter?
If it's a charger, the chassis bond wire is necessary to safely carry the charge current should the battery negative wire fault. Otherwise, the full charge current could be carried by the AC safety ground, which is undersized for that task. At least with a charger, the chassis bond is required by the NEC. It also provides some protection for other wiring should there be an internal DC fault in the inverter.
I don't think you need to worry much about ground loops in this particular situation. Absolute purity and noiselessness of the AC waveform is not needed (nor present at an inverter output, even a pure sine inverter output). Ground loops are more of a concern with things like audio or video signals.
The chassis ground tie should be directly bonded to the chassis, not the battery negative terminal. The battery negative to the inverter could be tied either directly to the battery or to the chassis, though going directly to the battery is often preferable as a lower impedance connection. The neutral line should, of course, be switched via the transfer switch along with the hot, since the RV should not have neutral and ground bonded together when powered via the shore power cord.
