How are people avoiding any fat?

It sounds like a number of reflux sufferers have sworn off all fat in an effort to get better. I've thought of trying that but wonder: since a number of vitamins are fat-soluble, wouldn't dropping fat from your diet result in nutritional issues?

I've actually added some fat in the form of coconut oil as it helps with my constipation - result of gastroparesis related to vagus nerve damage from my hiatal hernia.