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If I understand it correctly, they randomly decided to try starting the car immediately or to go wrap the wires first. This absolutely demonstrates a causality, they just didn't cleanly separate the different factors which changed.

Your comparison to placebo is very apt: Giving medication to a patient (vs not giving anything) causes them to get better, but it might be the "giving a pill" part instead of the "ingesting medication" part that matters.

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It doesn't show causality because their decision of when to do it wasn't random (so maybe when in the mood to go straight to wrapping wires they were also in the mood to turn the key slightly more firmly, or...), and also because there's no way of knowing if wrapping the wires was in any way relevant - maybe the vehicle actually just needed X minutes between unlocking and starting, and wrapping wires was a way to spend that time without using a timer, or maybe... who knows what other maybes!

And sure enough, their story concludes with discovering that there was no causality from the wire wrapping at all. It was just about killing time.

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