The "law" is mere empirical correlation - e.g. you are smarter than a blue whale.
The fantasy that the baby spiders with encephalization quotients (https://wikipedia.org/wiki/Encephalization_quotient) off the charts (because their brains displace their digestive systems and partly fill their legs) are more intelligent than humans, appeals to me. I suspect raw intelligence doesn't require many neurons. But spiders aren't social.
Parrots are.
I've always felt spiders are different from other bugs. The way they move feels more calculated
Lots of spiders spins webs. This requires very careful stepping, so you are quite correct, their movements are very calculated. They have to step on a high wire, possibly vertically, while avoiding the sticky parts, getting knocked off, hit by prey, etc
Your comment makes me wonder if it is indeed related to their relative intelligence to other insects.
I think it has been suggested that the "intelligence" of octopuses might be a side-effect of the huge amount of data processing that is required to control a body without a skeleton.
Also...brain size might be a decent proxy, but there is a large amount of variation in nature for distribution of neurons. Your brain is a centralized cluster, but we have neurons all throughout our bodies too. With octopuses, neurons are far more heavily concentrated in the tentacles than mammals, and they certainly show extremely high intelligence.