Al-Nawawī explains that the Prophetic wording “Whoever takes up arms against us is not of us” is transmitted through sound routes elsewhere. ʿAwf’s criticism concerns this attribution through al-Ḥasan: in his judgment al-Ḥasan did not transmit it in that fashion, or ʿAmr did not hear it from him.
Thus «ʿAmr lied» does not negate the hadith through every other route. Authentication of a report’s wording and validation of a particular chain are distinct questions.