How can one refute incorrect inferences drawn from the Hadith "Salman spoke the truth" regarding the uncovering of the face and the permissibility of intermingling between men and women?

If the hadith refers to uncovering the face, then this is to be understood as applying to the time before the revelation of the verse of Hijab, as Aisha (may Allah be pleased with her) said: "May Allah have mercy upon the early immigrant women. When Allah revealed: {And let them cast their head-coverings over their bosoms}, they tore their cloaks and covered themselves with them." Ibn Hajar and Al-Bagha clarified that "ikhtimar" here means covering the faces, and that this was before the obligation of hijab.

As for intermingling, merely a man speaking with a woman out of necessity, with assurance of safety from temptation and observance of proper covering, is permissible. Al-Mubarakfuri mentioned in his commentary on Al-Tirmidhi that among the benefits of Salman's hadith are brotherhood for the sake of Allah and visiting brethren, and the permissibility of addressing a non-mahram woman out of necessity and asking about matters that entail benefit.