No, that does not explain the subjunctive, because no reason or explanatory fact is introduced by the *quod*. Therefore Allen & Greenough's [§ 592][1] does not apply. Please note that the section you quoted refers to [§ 540][2], which begins thus:

> The Causal particles _**quod**_ and _**quia**_ …

But _quod_ is not a causal particle here. It does not mean “because.”

A simple example for causal clauses, as described by Allen & Greenough (but note that they have plenty of examples themselves):

> Profectus est, quod constitutum cum aliquo habuit.<br>
> *He set off because he had an appointment with somebody.*

He had an appointment—you have it on my authority.

> Profectus est, quod constitutum cum aliquo haberet.<br>
> *He set off because (or so he said) he had an appointment with somebody.*

He said he had an appointment, maybe he did, but I haven't checked.

----

If you wanted to use classic(al) indirect speech, you'd get rid off the *quod* and put the subject in the accusative:

> Memento et ipsum servivisse in Aegypto et eduxisse te inde Dominum Deum tuum.

(Who led whom out of Egypt? Awkward.)


  [1]: http://dcc.dickinson.edu/grammar/latin/intermediate-clauses
  [2]: http://dcc.dickinson.edu/grammar/latin/causal-clauses