Hazrat Hasan Basri (rahimahullah) once mentioned the following regarding the extremely high level of hayaa which Hazrat ‘Uthmaan (radhiyallahu ‘anhu) possessed, “He would be in his home, and the door would be locked, yet he would not remove his clothing entirely at the time of bathing (i.e. he did not remove his lungi when making ghusl, as is reported regarding the manner in which Rasulullah (Sallallahu ‘alaihi wasallam) used to perform ghusl.)”
(Musnad-e-Ahmed #543)