Funny how "barely false" the conjecture is: "in this graph, finding an upper path was 1/10^6500 percent more likely than finding a lower one — an unimaginably small but nonzero number. The bunkbed conjecture was wrong."
I'm a little disappointed that the brute force search didn't work -- it it had, I would have come away feeling like I could have done it myself.
Interesting read! I assume the hunt is now on for both the smallest graph where this is the case, and the largest discrepancy. It would be great if there was a graph small enough to make some nice art out of, or even just to fit in your head.