What if the chess position is mate in one move? Cases that are sufficiently special to ride the short bus do not make a general argument.
That would be in the "More Likely" bucket, or rather an "Extremely Likely" bucket. You said that the girl would say "hello" & that is in the "More Likely" bucket too, but far from a certainty. She could ignore him, turn the other way, poke him in the stomach, or do any of an almost infinite other things. Either way, you're resorting to insults & I've barely engaged with you, so I'm going to ignore you from here on out.
A stub on a point that's come up recently.
If I owned a paperclip factory, and casually told my foreman to improve efficiency while I'm away, and he planned a takeover of the country, aiming to devote its entire economy to paperclip manufacturing (apart from the armament factories he needed to invade neighbouring countries and steal their iron mines)... then I'd conclude that my foreman was an idiot (or being wilfully idiotic). He obviously had no idea what I meant. And if he misunderstood me so egregiously, he's certainly not a threat: he's unlikely to reason his way out of a paper bag, let alone to any position of power.
If I owned a paperclip factory, and casually programmed my superintelligent AI to improve efficiency while I'm away, and it planned a takeover of the country... then I can't conclude that the AI is an idiot. It is following its programming. Unlike a human that behaved the same way, it probably knows exactly what I meant to program in. It just doesn't care: it follows its programming, not its knowledge about what its programming is "meant" to be (unless we've successfully programmed in "do what I mean", which is basically the whole of the challenge). We can't therefore conclude that it's incompetent, unable to understand human reasoning, or likely to fail.
We can't reason by analogy with humans. When AIs behave like idiot savants with respect to their motivations, we can't deduce that they're idiots.