For 12v power ground is just a convenience.
For 120v power think of hot as the source and neutral as the drain. Ground is the secondary drain that provides a path during a fault so the power does not go through you as a drain.
Nothing is really going to earth ground especially with an inverter. If you are plugged in the ground connection is all you need.
Technically the frame of the panels should be grounded to the RV frame same as a home installation but few do it. More important if you have a series high voltage system.
If you want to conduct a direct lightening strike that would take a bit more effort. The strike will still jump to the earth and you should be unaffected.