Wow. I can't imagine what you're going through but I think that your intuition is correct. There have been studies that show cancer feeding off of sugars Does Sugar Feed Cancer?.
I would listen to the medical professionals but, me personally, I'd request that others refrain from feeding him the other foods and I'd focus on trying to provide him with better nutrition. Also, while I think fighting this with nutrition is a great approach, I'd also rely upon modern medicine and good medical practices. However, all of this is pure speculation as it is often easier said than done. Good luck and best wishes to your son. No four year old should have to endure that.