Something tells me that if we heard the other side of the story it might hit different. There's a lot of wiggle room in what "making his team members feel bad" could mean, and I would be surprised if constructively voiced criticism would have gotten someone written up.

With my experience of being written up for constructive criticism the reasoning was that I didn’t give constructive criticism to others and they felt singled out. I only give such criticism in private so of course they were not there to see the others. Apparently that wasn’t a sufficient explanation.