I am very lucky because my 4 year old is a fantastic eater; amongst the more "unusual" things she'll gobble down are the pickled baby octopus you get in a seafood salad, mussles, sushi, squid, sweetbreads, calves liver, mild curries, most fruit and vegetables, smoked salmon, anchovies, olives, Chinese food, rare steak, parmesan, gorgonzola and crab.
Granted, she has actually been exposed to all of this stuff and I do a lot of cooking from scratch, but I have never made an issue of it.
So ....... it may "appear" that the answer to an "unfussy" child is lots of different food experiences and home cooking but my older 18 year old son is nowhere near as adventurous, never has been, yet has had the same upbringing.
Worse ...... I was a "fussy" child. It wasn't a question of preferring a bar of chocolate to a plate of peas, nor refusing various options until I got the one I wanted but a combination of physical and psychological horror at the prospect of having to eat certain things: particularly fruit and veg. I would literally gag, and sometimes throw up if forced (eg. school cabbage - that showed them !) Even now, I can still remember the fear I felt at certain foods ...... it wasn't me being petulant, attention seeking, spoilt or awkward. The smell alone would often make me feel sick.
Then ....... as I got older, I gradually lost this fear and found the confidence to try new things (previously, this would have been impossible with the vomit reflex thing going on). I now adore onions, which was one of my particular hates, and eat most things (though not a lot of veg or fruit, I do eat some). In fact, I'd now say I have a very open-minded attitude to all sorts of food including raw fish, raw or rare steak, offal, very ripe cheese and so on.
I don't think the issue should be whether or not a child is fussy ...... I think it should be more about bringing that child up so their tastes (or lack of) don't make things unnecessarily difficult in social situations. I was very aware of being gracious, eg. at friends' houses about any food offered and to decline politely and not, for example, to demand anything else. I don't recall this was ever a problem but I can remember feeling petrified at the prospect of being put under pressure to eat something I literally couldn't when going somewhere new - thankfully I never was.