But that still doesn't equate to "cause". That may just be inexactness due to you trying to explain math to a pinhead (in fact, I'll give you the benefit of the doubt and say it is). But it's just that inexactness that's led to this discussion going on for two thousand posts.
What you mean to say, I think, is that the regression of normally distributed error towards the mean of the error can look like regression to the mean of the population. That's not a "causal" relationship...in fact, it's really not any sort of relationship, since you're talking about two independent statistical distrubitions. It just appears to be, to people like HA who think they're mathematicians yet can't define terms like "variance".