Is what is mentioned regarding specific supplications for each step of Wudu' correct?

What some scholars deemed commendable to say during ablution (wudu') is not actually commendable, nor is it legislated to utter it, because nothing of it has been authentically reported from the Prophet, peace be upon him. Every hadith (definition) concerning the adhkar (remembrances) said during ablution is a fabricated lie. Nothing has been authentically reported from him except the Basmala at the beginning, and his saying: "I bear witness that there is no god but Allah alone, without any partner, and I bear witness that Muhammad is His servant and messenger. O Allah, make me among those who repent, and make me among those who purify themselves," at the end of it.