This sounds like a complex case. I think this kid needs a bit of "tough love". This kid has used food as a way to control his parents . Being a poor eater obviously gets him a lot of attention form the parents, albeit in the form of anguish, frustration , despair. Nothing is going to happen until the parents give him some very clear boundaries. Consistancy is the key in my opinion. They seem more the indulging types. If they have trouble managing him at 3 this kid is going to be uncontollable in his teens.
Kids being human are always wanting to exercise some control over their environment. The way I've always managed the food issue with my daughter is to give her a choice of 2 things that I think she should have. Would you like apple or orange? She will usually reply chocolate, but I then introduce the third choice which is nothing. Then she ususally choses something on offer. I'm happy because she eats something healthy. She's happy because it's not a control issue and her hunger is satisfied; I'm not telling her what to eat, she is exercising soem control.
Another thing a MAternal Chiuld nurse told me is that kids will eat when they are hungry. If the kid throws a tantrum and refuses to eat they will usually eat if they are hungry.My guess with this kid is that he might hold out for a few days, but eventaully he'll give in. Sometimes if my daughter is a bit ferral I just leave food out on the bench and give her a bit of space. As long as I don't make an issue of it and remain out of sight she will go and eat when she thinks I'm not looking. She's happy, I'm happy.
It sounds like this kids eating habits are pretty ingrained, and I think it's going to take a lot of resolve from the parents to crash on through some major behavioural modification with this kid. They are going to need a lot off reasurance, but until they stop denyiing that there is a problem this kid is going to keep l;earing that he can hold his parents to ransom.
I get my daughter to help me prepare the food, then she is more interested in eating it. We make bread( occaisionally) or use vegtables form the garden. Home grown vegetables taste so much better and the broccoli and couliflower we harvest from our veggie patch taste sweet. I get my daughter to help harvest things from the garden and I'm sure that has helped her to eat healthy food.
Good luck. Hope this is useful.