Modified sinewave are actually stepped squarewaves.
The battery runs a high frequency (25KHz to 100KHz)switching DC to DC upconverter, usually producing about 150 vdc at its output.
The 150 vdc is taken to a MOSFET output bridge and chopped to produce the "modified sinewave" which is really a short across output plug for about 1/4 cycle, +150 vdc for 1/4 cycle, short again for 1/4 cycle, then reversed, -150 vdc for 1/4 cycle. The RMS of this is about 120 vac.
Problem is with this output bridge chopping there is no ground common to either side of output plug. On the above described sequence, the first short across the plug occurs by turning on the two top MOSFETS of the bridge tied to +150 vdc supply so both prongs of AC plug are at the 150 vdc potential. The second short across plug cycle is done by two bottom MOSFETS of the bridge tied to zero volts (ground) of the 150 vdc supply.
Now we get is dependancy on particular inverter. On the DC to DC upconverter there is a feedback from the 150 vdc output to the switching control on the battery side of the upconverter. This feedback can be simple resistor feedback, optical link or transformer link like most computer swithing power supplies. If you have the feed back isolation at least you have the secondary 150 vdc isolated from the battery side ground.
If you wire the modified sinewave inverter into your breaker panel you run into a problem with the bridge arrangement of the inverter. If you don't disconnect the neutral from the breaker box ground (white wire) then one side of the inverter plug will be connected to earth ground through your fuse box. If your inverter and battery are floating, not touching anything, it will appear to work. If you are grounded (standing on ground or touching fuse box) and touch the inverter case or possibly the battery terminal, you will likely get kicked on your ass.
Only really save way is to put an isolation transformer between inverter and fuse box.