If her parents give in to anorexic or bulimic behavior, that usually means they are enabling that behavior.
If such parents “don’t want to be the bad guy” by insisting on healthy living, there are family counselors often available, and they can play that role of establishing order.
Some families honestly may not know what to do, with the local equivalence of CPS lurking around any corner, ready to pounce on any strict parent.
Why should they ‘parent’? Greta is bringing them fame and fortune.