A correct prediction is meaningless because it wasn't accompanied by another correct prediction?

More or less. Think of it in terms of selection bias: a bunch of people enter a lottery of some sort. After the lottery concludes, the lottery organizer Yliezer Eudkowsky praises the winner, entrant #57, for their deep insights into lotteries and how to guess the winning number and admonishes everyone who told #57 to not get his hopes up. Do we now credit #57 for wisdom and study his numerology? No, not really.

Now, if #57 had simultaneously entered 5 other lotteries and won 3 of them, then we would start wondering what #57's edge is and preorder #57's upcoming book Secrets of the RNG Illuminati. Or even if he had won none of those other lotteries and simply gotten 3 near-misses (5 out of 6 digits right, for example), that would still serve as replication of above-average predictive accuracy and not mere selection effects, and persuade us that something was going on there beyond randomness+post-hoc-selection.