Here is my reasoning: start with two vertices u and v in the first floor and the vertex corresponding to v in the second floor (call it w). u and v are connected if, after deleting some edges randomly, there is still a path from u to v, similarly for u and w. But for any fixed path from u to w, you can get a shorter path from u to v by just going across between the floors one less time. Because a shorter path is more likely to survive than a longer one (by a factor of p), it makes sense that overall, the probability of some path from u to v surviving is larger than some path from u to w surviving. But, that reasoning breaks down, in part because when you drop the last crossing edge, there are many ways of adding it back in, so each path from u to v might correspond to many paths from u to w.