With no shore power and the inverter turned off (remotely or locally), there should not be a buzz. In this situation of "no shore power", the buzz (a 60Hz sound or its harmonic) means that the inverter is indeed drawing battery power.....to make the buzz.
Sounds like rather than a complete shut-down, the inverter is only going to a standby mode (no AC output, but none-the-less drawing some minor current from the batteries). It's almost as if your unit has been programmed to go into "standby" and never turn off. Your inverter user manual might help you reprogram this beast. Otherwise, you've got a inverter that's just "not listening" to your commands.
Input back to Rex:
Most (all?) large-current inverters are direct-connected to the house battery bank, thus not wired thru the battery disconnect switch. Did I read/interpret your posting correctly?
Robi & Dale ---- Go Navy ----
2016 Winnie TOUR 42'
Tow: '08 Buick Lucerne