In the heated debate over Turkey’s fraud-stained referendum, one particular narrative stands out: that the country’s 16 million or so Kurds played a considerable part in swinging the outcome, albeit narrowly, toward a yes. This, in turn, has prompted hopeful murmurs of a thaw in the frozen peace talks between the government and the Kurds. But Kurdish leaders dispute this version, saying it overlooks the fact that much of the alleged cheating took part in the mainly Kurdish provinces. Veteran Turkish commentator Rusen Cakir called renewed Kurdish support for government an “urban legend.”

The claim first came from President Recep Tayyip Erdogan shortly after the results were announced. Erdogan said, “When we consider the status of the political parties in the referendum, we observe a 10-20% increase in the southeastern provinces.”

He was comparing the percentage of yes votes in the heavily Kurdish region with the share received by his ruling Justice and Development (AKP) during the last parliamentary elections held in June and November 2015. A chart circulated by pro-AKP accounts via social media conflating the yes votes in the referendum with those won by the AKP stated that support among the Kurds for the ruling party had jumped by over 400,000 votes.

Presidential spokesman Ibrahim Kalin echoed the claims of a Kurdish boost in his column for the pro-government Daily Sabah. “By making a very clear distinction between the Kurds and the PKK, President Erdogan and the government have won the Kurdish confidence again.”