There is variation in the data that could be reflective of that time lag. If the population had no awareness of the effect and no ability to observe the impact

There is variation in the data that could be reflective of that time lag. If the population had no awareness of the effect and no ability to observe the impact of grain consumption on their children, then maybe it would proceed like some chemical process. But the population can learn and change behavior. My point is that your dismissal, in the way you framed it, is possibly just as much a random walk as the correlation in the way it is presented. Neither is conclusive.