Yes, yes, and yes. I appreciate your compassion for men who are victimized by false accusations. You clearly get what it's like, and I bet your empathy on this issue has benefited a ton from speaking with multiple men who've been through it.
My physically violent ex-wife at one point was maintaining that I was violent with her too, which there was zero truth to. Her willingness to lie about that gave her extra (sick and twisted) power in our relationship as I was disentangling from her. I'll never know what lies she may have told about me to her network of friends, family, and colleagues who got to know me during the 4 years she and I were a couple. Not a single of those individuals reached out to me during or after our separation to express sympathy or show interest in my perspective on things. (That's just a data point - not necessarily an indicator one way or the other that she spread lies about me to them.)
Also, I recently reconnected with a friend from high school. He shared that back in high school - 10+ years ago - a girl spread a rumor that he raped her. (I don't remember hearing this rumor back then.) Their sex was consensual, he says, and I believe him. He has continued living in the same town where we went to school, and for years he has lived with this worry of not knowing who in his town heard that rumor and believes he is a monster who rapes girls. This was my first experience hearing firsthand from someone I'm close with about withstanding this kind of reputation damage. As he conveyed this to me, it was clear from his tone of voice and body language that his suffering was real.