The recommendation of performing wudu' for one who touches his private parts without desire

I heard that it was narrated from the Prophet (peace and blessings be upon him) that if one performs wudu' and then takes a bath, his wudu' remains valid; however, a person may perform wudu' and then take a bath, and during the bath he may break his wudu' or his hand may touch his private parts, which invalidates his wudu'!
Touching the private parts does not break the wudu' unless it is done for the sake of desire; as for touching it without desire, the wudu' is recommended (mustahabb) and not obligatory. Accordingly, if one takes a bath after performing wudu' and his hand touches his private parts without desire, his wudu' is valid.