Is silence regarding the correction of sayings attributed to the Prophet, peace and blessings be upon him, such as the saying "People's رضا (pleasure/satisfaction) is a goal that cannot be attained," considered a mistake, knowing that they are not authentic hadiths, in order to avoid embarrassment?

Attributing words to the Prophet, peace and blessings be upon him, that he did not utter is a grave evil. The Messenger of Allah, peace and blessings be upon him, said: "Beware of narrating too much from me. Whoever narrates from me, let him say what is true or authentic. And whoever attributes to me what I have not said, let him take his seat in the Hellfire." Therefore, one must object to anyone who attributes a saying to the Prophet, peace and blessings be upon him, that is not a hadith, and inform them that it is an ancient saying, or a wisdom, or a saying of a scholar. Otherwise, one who remains silent risks sin.