Zvarych blames it all on the fact that he never reads about himself: if he had, he would've issued disclaimers a long time ago.
Here's what he says about his degree (quoted in Ukrainska Pravda, in Ukrainian):
[...] I don't have a master's degree from Columbia University. Instead, I have a degree that corresponds to a master's from Columbia as well as from any other scientific institution. If I didn't have this level of scientific knowledge, I wouldn't be able to get an invitation from New York University to teach there.
When I was asked right after my move [to Ukraine], "What's your degree?", it was hard for me to explain and draw analogies. I explain it this way: "I have a bachelor's degree. But I've also taught and had a professor's title at New York University." They ask me: "Wait, and what was your scientific level that allowed you to teach at New York University with such a degree?" And I explained that my degree equaled a master's degree. [...]
I wish someone explained to me what kind of a degree Zvarych is talking about. Maybe it's something untranslatable - but he could at least have named it in English...