You need to realise there's a difference between actually earthing something ie making a connection to plant earth and taking one of a pair of floating power terminals ( like those from an
inverter) and connecting it to the earth pin of the mains outputs that it serves.
So dealing with the latter first:
Normal mains wiring in a household comes from the output of a local transformer and as such would float and would have no live or neutral and you would be safe to touch either wire ( but not both together) but the leccy board connect one of the power supply cables to planet earth, this cable now becomes a neutral and the other becomes live. If you now touch the live while you're standing on planet earth current will flow through the live cable, through you, through planet earth and back to the neutral completing the circuit and giving you a belt. This wouldn't have happened if the leccy board hadn't have earthed one of the output cables.
The output from the
inverter is naturally floating, it has no live (and therefore no neutral) you can touch either cable and you won't get a shock, in order to get a shock you need to touch both wires simultaneously. This (typically) makes a floating supply very safe, for example you MUST have a floating supply where you have a power outlet in a bathroom at home, this is accomplished via a 240V isolation transformer that sits behind a razor socket.
So, why did they ever earth that pesky cable and create a LIVE? The problem with floating or isolated supplies is when you have more than one socket outlet connected to the same floating supply, ie connecting your van
inverter to multiple sockets in your van, I'll explain..
Imagine a floating supply, remember no live and no neutral just 2 cables supplying 240v across them. Let's call these 2 cables Hot 1 and hot 2 and remember you can't get electrocuted unless you touch both simultaneously.
So you have a toaster with a metal case, it develops an internal fault and hot 1 shorts to the metal body, what happens? NOTHING! Unlike the system where they created a live and a neutral by earthing and output a
fuse doesn't blow because theres nowhere for the fault voltage (in the casing) to go to. The user is oblivious, they keep touching the case but nothing happens because they're only touching Hot 1 and not Hot 2 as well.
Now consider the same kitchen and now the metal kettle develops a similar fault but this time it's hot 2 that gets connected to the metal body by a fault. Again nothing happens and no one ever notices UNTIL someone touches the toaster and the kettle at the same time, that person is now touching hot1 and hot 2 simultaneously with probably 240v across left hand and right hand with current flowing straight across the heart, hopefully muscle contractions will break the connection but if not you're dead.
The above can obviously only be an issue if you have 2 or more items plugged into the same
inverter at the same time, using a single item doesn't present a risk.
So if you're wiring your
inverter into your MH 240v system and you intend plug in more than 1 appliance with metal parts then you could protect yourself from the above and create a LIVE and neutral setup by connecting the left hand pin of the output socket to the earth system of the 240v wiring. I'll be honest and say I haven't bothered because every time we go on EHU the appliances are effectively tested against such faults and if had a live to earth or neutral to earth fault they'd blow a
fuse or take out the RCD, in other words the appliances are regularly tested for faults.
Earthing the
inverter, ie connecting the case of the
inverter to planet earth??? What could that achieve???? Pointless I'd say.
Connecting the earth pin of the
inverter to planet earth?? Why? Again pointless, it's probably not connected to anything internally anyway.
I guess there could be a scenario where the
inverter develops a fault and hot 1or2 gets connected to the case of the
inverter but connecting it to planet earth wouldn't achieve anything but connecting the
inverter case to the earth wiring system within the van possibly wouldn't be a bad idea, I'd have to think about it