I know I'm very late to the party, but one thing that might help: You appear to be under the impression that there are three sources of randomness in your model: $S$, $E$, and $u = S - E$, where $u$ is the proxy measurement error. This is not correct. There are only two sources of randomness in your model. They are (in a typical setup), $E$, your latent variable, and $u$, your proxy measurement error.
$S$ is a random variable, in the sense that it is equal to $E + u$, ie the sum of two random variables. However, because $S$ is uniquely determined by $E$ and $u$, it follows that $S$ is not a source of randomness. So to discuss the dependency between $u$, $S$, and $E$ is not really meaningful, because at most only two of these three random variables can be a source of randomness in your model.
Note, in a typical framework, a common assumption is that $u$ (proxy measurement error) is independent of $E$ (latent variable). Your framework appears odd in that someone has told you that your proxy measurement error is independent of $S$. We could, of course, set things up this way, by assuming that $u$ and $S$ are the sources of randomness and that $E$ is uniquely determined by the two of them. But, as I said, this is an odd way of doing things.