Let me refer you to your original post. When you use terms such as "religiosity" and "intelligence metric", you are referring not to individuals, but how religious (or intelligent) people are in groups. If I wanted to measure the religiosity of my town, I would ideally ask everyone in the town to fill out a survey, or interview them regarding their religious behaviors. If I didn't have time to survey everyone, then I'd try to randomly sample proportionally from different neighborhoods. Either way, I'd get an average number. That average number would be an indication of the religiosity of my town.
The point being, when you use the word religiosity, you're referring to a group of people. If you're comparing a trend in religiosity to intelligence, that's also referring to a group of people. Whenever you're looking at groups of people for trends, you're using statistics.
The mistake you're making is that you're taking information from groups of people and trying to apply it to individuals. This is wrong. I can show a definite correlation between lung cancer and smoking heavily. This does not mean your Uncle Frank who smokes two packs a day is going to die of lung cancer. Uncle Frank may not even have a hint of any cancer and live to the ripe age of 102, smoking like a chimney. This doesn't mean the statistics are wrong, or Uncle Frank is wrong.