You can call him a snowflake all you want but seeing the situation he's in, totally normal human emotion to act out this way. Imagine how you'd feel if you had issues with your boss who kept delaying your promotion then tried to delay it more by basically implying you have mental health issues. Even if Tony does have mental health issues, any sane person would be fucking livid in his situation.
What Dana said was offensive and implied Tony was wearing sunglasses indoors to look cool(and you know deserved fucking physical harm for bad fashion). Seeing how much the dude has likely suffered cause of what happened, imagine your boss mocking you about such an experience when what he's saying isn't even true?