My layman's understanding mirrors this. Because one part of a pair of virtual particles crosses the horizon, and the other one does not, they become separated

My layman's understanding mirrors this. Because one part of a pair of virtual particles crosses the horizon, and the other one does not, they become separated by said horizon and cannot recombine and disappear. The particles become actual and not virtual, but one is lost to the hole. Hence, it looks to the external world as if a particle was emitted by the hole. Note that to my (layman's) knowledge, this has not been actually observed, but does seem to be a modern consensus and involved a paid bet.