Europe and the EU are getting conflated more and more. It's kind of like how if someone said he's American, you wouldn't assume he's from Brazil, even though technically Brazilians are American since they're from the American continent or continents.
Whilst he's wrong from a geographical perspective, I assumed in good faith that he was talking about 'Europe', the political institution - which he'd still be wrong about. The UK is still part of the EU until it isn't.
In a political conversation the geographic meaning of Europe is usually significantly less useful than the political one. So this is not surprising at all.