Your quoted manual reference raises a good question. I do not know what the ramifications would be, if any, using an ungrounded neutral power source tied to the original neutral buss. Installation would be much simpler. My main panel breakers open both hot and neutral. With neutral open on the feed, I do not know where my ground to neutral would originate. I am approaching the inverter installation as a power source just as the generator with neutral and ground at the source. As I have already identified 4 of the 6 neutrals for the circuits the inverter will power, I will continue that direction.
The neutral-ground tie is ALWAYS at the power source. If you are connected to shore power, the tie is at the originating panel for the circuit, wherever that may be, but it is on shore, NOT on the boat. If you're running a generator, it will be at the generator, and any switch that changes source from shore to generator must also handle that ground-neutral connection properly. If you are using an inverter, then the tie-in is at the inverter, the source. Marine inverters have a relay that makes that connection when inverting, and breaks it when passing through. It can quickly get complicated, and particularly if you have a boat that has co-mingled neutrals.
If you have an inverter powered while connected to shore power, it will connect neutral-ground, creating a path to ground that is a fault. If your shore power is via a GFI or ELCI protected circuit, that fault can trip the breaker. Many of the new ELCI shore power systems have a central trip point, so if your boat has an improperly connected neutral-ground tie, you may trip the ELCI on shore, and it will more often than not, drop power to whatever's connected to that main breaker- read: a whole pier or multiple piers. This always happens when it's hot, everyone's running A/C, and the marina staff who have the key to the main panel access have gone home for the long weekend. You'll make friends fast!
Thus the caution about connecting all neutrals to the neutral buss for the inverter. If you're contemplating installing an inverter, it would be wise to include some allowance for a MARINE electrician. Not Jim-Bob, the guy who wires houses, or even a commercial dirt electrician, as the marine world is not in their experience sphere. Most have NO CLUE. Ask them about co-mingled neutrals, they'll give you a blank look, since in their world, neutral is neutral is neutral.
Improperly wired AC on a boat is nothing to trifle with, it can cause stray current to enter the water, and create an electrocution drowning condition. Any new inverter install should be completed by, or at least checked by a competent ABYC marine electrician to insure there's no leakage to ground. If you have an inverter, and you trip an ELCI or GFI breaker, it's cause to have an electrician check it.