Your question is more general than the excerpt from the book. If I understand it correctly, "it is bad to multiply two expectations of the same variable, as otherwise the sample of the product [of the variable with itself] will be biased."
This amounts to saying
$E[x^2] \ne E[x] \cdot E[x]$. Now this is indeed the case in many situations.
Consider that $x$ is normally distributed with mean $\mu$ and variance $\sigma^2$, then $E[x^2] = \mu^2 + \sigma^2 \ne E[x] \cdot E[x] = \mu^2$. So indeed, there is a constant bias by $\sigma^2$.
Is it that what you were asking?