Kurt,
I can't answer for Dave but in the case of Heartland's OEM installation of the residential refer, there are two 12 volt batteries in parallel and they are NOT dedicated to the inverter. As Dan indicated, Heartland does not have a long enough timeline of usage of this configuration, so real world runtimes are not yet known. It's encouraging to hear from Dave though that on his retro-fit of a smaller residential refer, he's run 14 hours on inverted battery power.
If my camping style had me boondocking for a day or 2 max, a few times a year, I'd strongly consider a single 100 to 150 watt solar panel mounted on the roof and a solar charger/controller ($500-$1000 for the kit) - all to keep the batteries topped off or as much as is possible given solar conditions.
A good question too would be, what's the average rate of discharge of the batteries when they are inverting power for the refer and how much power can a truck charge line really put back into the battery bank? I have no idea on this. If the rate of discharge is significantly higher than the rate of charge from the truck's charge line, then a solar panel could also be really useful during travel, especially enroute to a boondock destination. Be nice to arrive all charged up