There is no reproach for the Prophet in that which Allah maketh his due. That was Allah's way with those who passed away of old - and the commandment of Allah is certain destiny -
Times are computed by method; your mosque's timetable governs the adhan. Every text carries its source and grade. Nothing here is a fatwa, a prediction, or a substitute for a doctor: your own scholar decides what is contested, and the tradition itself says the practice is alongside treatment, never instead of it.