We have a 19 month old who is now off the bottle and eating/drinking age appropriate foods. But, it was a long process...
I can tell you right now that if you have not had a child with eating challenges than you should not be offering advice.
We wanted her to eat with all our hearts, but there was a lot more to it than that. She ended up having a really (still does) strong gag reflex, apirating, and just plain not knowing how to swallow food. She would either gag and throw up everything, or chew on something for 30 minutes. NOTE: She did much better when we gave her the food to put in her mouth or we just put it in her mouth (the spoon made her instantly get sick). She could not eat any baby food nor solids, until around 1 year old. Once she could eat some solid foods (cheese, yogurt, tiny pieces of bread), we started trying to wean her from the bottle. At around 16 months, she figured out how to drink from a sippy cup.
If you decide that you want to be there for this child, I suggest you make a list of foods... and keep trying... I also think sitting him next to the others, while they eat, may help him to see that it's OK to eat.
NOTE: She was NEVER able or willing to eat any type of rice cereal. I think the texture bothered her...
It's very easy to judge other people. I do not know the mom of this child. I doubt, if she is working and can pay a sitter, that it's a money issue... Maybe she just doesn't know how to deal with something like this? You might try finding some information about development at this age. Show the mom in a nice manner the info. Tell her that ECI will help (they helped us). They were great with suggestions and to just listen to our frustrations.
I would also tell her to go to another Pedi, to get a 2nd opinion. Our daughter ended up in the hospital twice with our 1st Pedi. She is doing great with the new one!
In conclusion, it's very easy to judge others... but, this type of situation can be extremely stressful. I am sure anything that you can do will be appreciated (if not now, in the future). Just do it for the child! :)