That could be it, although I really hate the word boundaries when it's just more like what people do in real life when they say what they want/don't want from others. And yes, he could give the emailing a chance without anticipating violations of his code.

My therapist is on vacation, but she said she'd be glad to reply to any emails I send, adding they would be short and probably very delayed, but that she would be glad to do that. She did not make a big deal out of it. I hope yours can ease up a bit and get over himself. It's not wrong to want communication when you're struggling.