A lot of assessment at a young age is done through parent questionnaires and conversation. If the parents are downplaying what they see (on purpose or through denial) then a doctor may very well say the child is shy. Because the doctor is not seeing the child perform the tasks but the parent is saying that the child does do it at home.
It is up to the parent to give a clear, accurate, unbiased assessment to the medical professionals when help is needed. Unfortunately a LOT of parents are in denial and are not able to do this...which hinders an accurate assessment.
You need to make a call. Are you willing/able to keep this child on and continue as is? It is NOT your job to 'fix' the child or make the parents see the light. You merely need to provide loving care and as many opportunities as you can without taking on an extra burden. Should you want to go above and beyond what is part of your job you certainly can and the child will benefit but ultimately it is on the parents to acknowledge your concerns an find extra supports to aid the child along.
A child as you describe above would benefit from being in a daycare center where there are multiple staff members and more resources to not only support his higher needs but to help inform and educate the parents. You are on person, with many daycare children...your time and resources are limited.