TOM in NH: good point, and good reminder.
the problem you report (blown inverter from improper grounding technique) is probably something that should wind up in the Newbies section. . . ? Truly a case where being excessively safe is not a good thing.
for the rest of you. . . even in cases where you're using a permanent-installation type of inverter, DO NOT, under any circumstances, make a connection between the AC section and the (lower voltage, floating input) DC section. DO Not even to ground the battery bank if the AC side is also grounded. . . those of you with lightning protection in your systems might want to check the resistance between the batteries and the grounding point for the lightning suppression unit before undertaking any grounding or permanent inverter installation project.
the exception, of course, would be if the manufacturer's installation manual explicitly calls for grounding both input and output.
defeating the isolation between the sections of your inverter, at the minimum, will make the inverter ineffient. . . other outcomes including electric shock or fire are possible depending on the exact details of the installation.
if you must ground the inverter, and if you have to choose one section of the inverter to ground, make it the AC side. . . subject to the above about grounded battery banks, and the below about 'floating' outputs. Grounding some inverters could be less safe than not grounding them. (grid tie and grid-charged UPS types are obviously designed for some form of grounding, and will be appropriately equipped. Plus their manuals will have some advice on the subject)
to check to see if your inverter will benefit from grounding: with a meter, check to see that the case of the inverter is not connected to the battery terminal/s (should be 100s of Kilo-ohms at least, better if meg-ohms.; no reputable inverter I have encountered has failed this test.)
Also check to see that niether of the AC lines is connected to the case (meg-ohms again) and DO NOT USE an inverter that fails this test. . . .
Check also to see if the 'ground' prong of the outlet is tied to the case. in many situations it will be, and this is acceptable, even good.
If the inverter passes those tests, then you can tie the case to ground for peace of mind without damaging the equipment or yourself. But, unless the inverter case is factory equipped with a grounding screw or grounding stud, you will not gain much by tying it down.
with the common portable sort of 120VAC inverter, there is no 'true' neutral in the system; instead each leg of the AC is about 60 VAC off the case potential, which serves as sort of a psuedo-ground.
Grid-tied House wiring, however, is usually done with the neutral bus tied to ground in the service entry panel. . . so if you hook the common (portable) sort of inverter up as temporary power, one side of the (normally floating) AC output becomes a ground reference. . . . which might lead to problems if there is a ground fault in a piece of equipment in your house and the inverter is grounded on the wrong AC leg, or if the isolation is defeated. (problems, in this case, being defined as short circuits and ground faults of varying severity. . . anywhere from 'tingle' to 'smoke.')
If you are designing/building a off-grid house from the get-go, your grounding arrangements will (obviously) have to be whatever makes your building inspector happy, and may involve some compromises in the inverter installation. . . . just be sure that you don't wind up with a floating AC output terminal and the inverter case both tied to the same bus.
hope that helps more than it hinders!
-Dan
