Can the wording of a referendum question change the result?

Yes, wording can change the result, and electoral bodies and governments act as if it can. A question that hints at an answer is called a leading question: it suggests a particular answer, and the person asking it expects agreement. Even a neutral-looking question can steer people through word choice, framing, assumptions and form.

The clearest case is Scotland in 2014. Under the Edinburgh Agreement, the Scottish Parliament chose the wording and the Electoral Commission reviewed it. The Scottish government's preferred question was "Do you agree that Scotland should be an independent country?" The Commission tested it along with three other versions and found that the "Do you agree" opening made it a leading question, more likely to get a positive response. The question was changed to "Should Scotland be an independent country?", which the Commission found the most neutral and concise of the versions it tested.

The same body did something similar for the UK's 2016 EU referendum. The bill first asked "Should the United Kingdom remain a member of the European Union?" with a Yes or No answer. Research found that members of the public felt the wording was not balanced and perceived a bias, so the Commission recommended a change, and voters ended up choosing between "Remain a member of the European Union" and "Leave the European Union".

None of this proves that one wording would have flipped one result. It shows that people who run referendums treat the question as part of the fairness of the vote, and test it before anyone casts a ballot.