This is something of a minefield and I am not very keen to get involved.
I have no real idea of the inverters available in N America so I can only comment on what I have found in the UK.
Here our supply is derived from a 3 phase 415v system with neutral grounded. One side of the 230v is grounded ( neutral ) at the supply transformer. The phase leads are live at 230v with reference to neutral.
I haven't had a great deal of experience with inverters ( playing as a hobby I can't afford them so I only see what I have fitted for others). All the cheap modified square wave things use a H bridge to chop the high voltage dc into a series of square pulses. The dc is isolated by the converter transformer from the battery supply and the ac output is completely isolated from the input and the case of the inverter which has a ground connection. These seem to be aimed largely at the car and camping market and they suggest you ground the inverter case. The load is assumed to float and the inverter transformer should be more than adequate to provide safe isolation. You can't get a shock from the output unless you touch both leads which in most cases should be impossible. Whether you can convince the stupid safety law makers it's safe is another matter. I think there is some special case for isolated systems for portable generators but I keep clear of the legislation.
Most of these inverters will run perfectly happily with one of the output leads grounded so it you tie it to a normal house wiring system it will still work. The neutral and ground are then linked just as for a grid supply. There is absolutely no way that any of the small inverters will blow a fuse and if you want fault protection then you need to use a RCD breaker that trips on differential current. Even most small engine driven generators don't have enough fault current to blow fuses and again they need similar treatment.
The only sine wave inverters I have met also had isolated output and a ground to the metal case. The filter circuits are invariably grounded to the inverter case and you should ground it to keep RF interference at bay. The Ones I have met are perfectly happy to let you ground one output lead.
There are older generations of inverter that use transformers on the output but I haven't met any for a long time although some of the high price units may do so ( I haven't played with them).
The world is geared to the grid system and most of the legislation is based on it, you open a minefield with isolated devices but personally I think they are safer but convince the man!
I think things are rather different in N America, the 110v system works the same way but the 220v is not from a 3 phase but from a split single phase with the centre point grounded. If you try to use a 220v inverter there is a problem in that the mid point of the inverter output gets grounded. If it is completely isolated then it will work on 220v and you can ground the case for the interference suppression. There is no way you can take any 110v load from it and all loads must be 220v unless resistive and completely balanced about the 110v.
If there is any form of internal connection from the inverter output to elsewhere then there will be a fry up.
I have never met a 60Hz 220v inverter so I have no idea if it is different from the 230v 50Hz ones.
I try to avoid this area like the plague. I have seen things installed by those who should know better that look to be complying with all the legislation bur some of it has been pretty dangerous if you stop to think about it from first principles rather than just blindly follow grid practice. What I do and what I tell others to do may differ.
Flux