I can't imagine a parrot starving to death as long as they recognize what's offered IS edible. I suppose mine has a varied diet because I would offer things that I was also eating. I made his first fresh foods seem more like me sharing with him than just dumping it in his dish and letting him figure it out. His main diet is fresh fruit/veg/starches.
He came to me on a seed/pellet diet. He already liked seed mixes & peanuts but would pick through his pellets, eating only his favourite colours first. But if I am patient, he will eventually even eat the pellets in the non-desirable colours. I consider seed/pellets as treats -- not his main diet.
With fruit/veg/rice/pasta... I guess he figured it out that this was what was being offered and relented and tried the foods I feed. Seeing me eat the same foods helped a LOT. He's so healthy, with good feathering and bright eyes. Patience works.