No they haven't lied - they have stated they have agreed to settle the debt
It does not stop the winding up application - that is a matter for the court to decide, as there are other costs involved, e.g. Barrister costs for the Statutory Demand, court lodgement fees, on-going legal costs - once the process starts the only party that can effectively stop it is the Courts - and if there are others who petition for the winding up well ... (DYOR)
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