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There may be a balance between how he experiences things internally and how others perceive them, an ideal solution would respect both views and help develop perspective taking or theory of mind for all kids involved.

I wonder how to help that happen?
Theoretically any interaction which is not successful has this at its heart... not mean-spirited or an attempt to undermine, but a simple difference of legitimate perspectives. If the teacher becomes aware of something amiss, hopefully gently probing questions would be asked to arrive at the different perspectives and help draw out the children to explain their views. Clarity in one's own position and the ability to listen actively are essential life skills for interpersonal problem solving, advocacy, negotiation.

A parent could also have similar discussions with their child at home, asking what was good and not-so-good in the child's day... asking the child about his/her own thoughts and feelings... and what others may have thought/felt, based on factual clues: what they said, and what they did. This can help a parent ascertain whether the child's social skills are weak, emerging, or strong, and whether the learning environment is impartial or biased against gifted.

There is a website dedicated to perspective taking. A web search on perspective taking or theory of mind shows more information and resources.

Tangently related, the book on confidence in this post comes to mind.