I think it's the exact opposite. Direct democracy would lead to people voting for what they want much more granularly, whereas the Brexit vote was once-in-a-generation opportunity that conflated many many different issues (immigration, "ever closer union", single market, London vs. the rest of England, England vs. Scotland, economic inequality, ...). I people were given a chance to vote for each of these issues separately, I would expect much saner (and less contradictory) outcomes...