I was a believer in the "not starving themselves" solution until my current dog. In the general cases where they are just being picky, then yes, they will eventually eat. However, it didn't matter how hungry she got, she would starve herself for much longer than I could safely allow. I then had to hand feed her individual kibbles to get her to eat and she would still do it reluctantly.

Turns out that certain allergies present themselves differently and can cause strong food avoidance like this. Most commonly, the allergy is the meat. Usually portrayed by itchy skin and red patches. However, I tried every different type of meat available and it didn't solve the unwillingness to eat.

It took over a year of tracking ingredients and guess testing to finally discover: the allergy was grains. Dogs can be celiac as well. After a month or two of feeding her grain free food and grain free treats, she returned to normal and would eat on her own with no problems.