I didn't followed this discussion the first time round, tbh, but if it's being resurrected then my opinion is that it's part of the responsibility of the parents to care for their children and control their eating until they're old enough to do it themselves, and to educate them enough so that they are at least theoretically capable of managing when they become more independent. Letting your child starve if you have the power to feed them is obviously abuse - and I maintain that letting your child get so fat that it constitutes a health risk is also a form of abuse. It's neglect on the part of the parent. It *is* hard to eat healthily, it takes a lot of discipline and effort and sometimes it's just so much easier to bung a packet in the microwave or order out or whatever. But while an adult can make those decisions for themselves and understand the choices they make, a child can't. Children are naturally greedy and want to eat sugary, fatty foods, and so it's up to the parents to feed them properly just as much as it's up to them to get the child to bed at a reasonable hour or see that she's properly clothed.
I'm going to use an example from my own life, which isn't perfect but I don't have anything else to hand. I'm a very greedy person, always have been, but my mum always made sure that we had a home-cooked meal once a day, cereal for breakfast, had rules like one packet of crisps OR two biscuits a day and no more, no fizzy drinks unless we bought them with our pocket money and then only one a day, and take-away once a month. We snuck sweets or pop, of course, as most kids will, but the rules were there and generally speaking we stuck to them. It doesn't take much to raise a child with a healthy diet, and a failure to do so - especially a failure to do so over *three years* is astonishing and I think does speak volumes about these people's parenting.