Yes, I'm afraid I can vouch from my own experience that ACL tears can happen without cutting or pivoting. My first (partial) tear happened when I landed awkwardly from a jumping sidekick while kickboxing, and hyperextended the leg. I didn't pitch sideways at all; the leg just bent the wrong way and then buckled under me. Four years later the ACL finally gave way completely when I fell backwards on top of my own skis after mistiming a jump, and slid down the hill. Again, no sideways motion at all; this time it felt like the weight of my body on the tail of the skis held me back while the rest of me was trying to slide forwards, and the two opposing forces just pulled something in the knee apart.
I'm not sure how common this is, but from my understanding of the mechanics of the knee I think that while it's far easier to tear an ACL with a twisting movement, an excessive movement of the shinbone away from the thighbone could have the same effect. Although it's far more common in skiing to tear the ACL when the binding fails to release and the ski twists the knee around, the second most common way is the kind of backwards fall that I had. I don't think there's any inherent weakness in the ACL that causes this; it's more the pressure that the joint is put under. If you think about the pressure of your own weight and someone else's, that's pretty substantial. Additionally, you mention that both accidents happened while you were exhausted; this makes sense, as the leg muscles provide additional support for the knee when it's under pressure.
I'm really sorry that you're facing another surgery. Good luck with getting the new injury sorted out - I hope your recovery is smooth.