If the parents have done anything wrong it’s going public, putting themselves in the firing line for abuse from the ignorant. This may seem a simple case of bad parenting to people who know very little about mental illness or children.
The fact is that when a child (or adult) has it in their head that they’ll only accept certain things as food you have no choice but to give it to them. No choice apart from force feeding, that is. And force feeding someone in that condition isn’t going to cure them off it; make them worse more likely.
And while we’re at it, don’t think of blaming the parents for allowing their child to get into this mental state. It happens in the “best” of families and in otherwise perfectly normal adults.
Sometimes we call a firmly held belief in something that isn’t true, based on available evidence, psychosis. But we’re not consistent. In fact, certain groups see such beliefs as virtuous. A believer in the existence of a supreme being is described as pious. Fringe political group work on conspiracy theory too, sometimes breaking their nonsense into mainstream thought. We know communism doesn’t work, but some will keep the red flag flying based on all sorts of excuses that it just hasn’t been done right before.
Meanwhile another group have convinced themselves that Covid-19 is some kind of hoax. It’s a widespread problem, and not just in uneducated communities; a quick look at the evidence is all you need to prove otherwise, but using selection they can make a case that’s good enough for them.
If your misplaced belief has an appropriate number of adherents it becomes a religion or political movement, and gets equal air time on the BBC. People use the idea that if others agree with them, they must be right and no contrary evidence is considered. It was probably made up by those seeking to undermine the “truth” anyway.
If, however, you alone believe there are aliens living in the house next door, you have a psychotic disorder.
So, before we jump to conclusions about mental illness, and in particular psychotic beliefs, perhaps we should first evaluate what we believe against the evidence.