I think what this thread reinforces is just how emotive eating and mealtimes can be. Again just reinforces my point that so much of children's response to food is nothing to do with the food itself (proved by the fact that most children reject new foods before they've even tried them). Food is offered as a form of nurture and love by parents but also turns into a source of conflict and control and anxiety. If children reject food it's just as likely that they're doing that because they want to get some kind of control/ assert their identity which is a very normal part of growing up the same way as kids might want to choose their own clothes or whatever (my dd1 went through a phase of refusing to wear trousers!). Of course, children go through picky phases just as they go through tantrums and phases when they want to wear the same shoes every day or whatever. The important thing is to remain positive about food, keep messages consistent, provide role models and so on.
Just so nobody gets the wrong impression. My kids were not born good eaters. I've had the same issues with them that every other parent has. The dds don't come to the dinner table saying, 'ooh, there's an unusual looking vegetable I've never tried before I'd love some of that mummy,'. Dd1 (5) still occasionally refuses some foods. Rice, for example, weirdly. But we have strategies for dealing with this. We might make a risotto for example with rice and prawns (which she loves) and then she eats it up but the main thing we do apart from eating together the same things is to keep repeating the hurricane mantra, 'OK, dd1 if you try it and don't like it just eat the rest of what's on your plate and leave the rest,' We do not have any more discussion about it and give it no more attention instead moving on to another conversation. 9 times out of 10 when we look around at dd1's plate (which we don't need to do obsessively because we don't do that hover, shovel, wipe thing which a lot of mums do who don't eat with their dds and is so incredibly off-putting) then she's eaten almost all of it.
By the way of course it's possible for siblings with the same parents to have different attitdues to food and eating. Of course, parents treat their kids differently esp. boys and girls and PFBs and last born children. If you speak to my sister (as PFB) she has a very different perspective of her childhood and our parents' parenting than I do. They were much more strict and controlling with her as the PFB. Arguably she had a much harder time. I'd so no coincidence that she's the one with mild food issues and I'm not.
And of course kids are influenced by their peers (one reason why I hate fussy eating because they end up influencing my kids and making them thing that they're the weird ones for liking vegetables for example) and by schools and by advertising and so on.
So, yes, of course, a parent can be doing all the 'right' things to encourage healthy eating and still have a child who is occasionally or always fussy.