Nietzsche is happy to take the Stoic phrase of "according to nature," but isn't happy to use the Stoic view of nature. Instead, Nietzsche substitutes his own view, pretending as if the perspectives are one and the same.
It's hard for me to believe that Nietzsche didn't know enough about Stoicism to understand that he was arguing in bad faith. Despite presumably knowing better, he falls into the same misunderstanding that most novices do about Stoicism - that it somehow glorifies indifference at the cost of purpose, mercy, justice, regard, and so on.
"Indifferent" is a dangerous word to use in this context. Here I use it in the contemporary sense of "apathy." But it's important to note that "indifference" to a Stoic is more subtle - meaning neither good nor evil (or - dare I say - beyond good and evil), but not implying actual apathy.
Stoics did not view nature in this way. Most notable Stoics believed in Zeus - and consequentially in intelligent design. They held reverence not for an empty, random, and nihilistic nature, but for one of purpose, order, and beauty.
It's clear by observing the life of any notable Stoic that they valued the same qualities Nietzsche accuses them of disavowing. Pairing Nietzsche's criticisms alongside the very first book in Marcus Aurelius' Meditations:
Are Stoics really "profligate" (wildly extravagant/shamelessly immoral)?
> From my grandfather Verus I learned good morals... From my mother... simplicity in my way of living, far removed from the habits of the rich.
Are Stoics really "without purpose and regard"?
> From Apollonius I learned... undeviating steadiness of purpose
Are Stoics really "indifferent without measure" or "without mercy and justice"?
> From my brother Severus, to love my kin, and to love truth, and to love justice... a polity administered with regard to equal rights and equal freedom of speech, and the idea of a kingly government which respects most of all the freedom of the governed
Indeed, Nietzsche is so far off the mark that he would have benefited from observing the same virtues that Marcus enumerates:
> From Rusticus I received the impression... to abstain from rhetoric... and to read carefully, and not to be satisfied with a superficial understanding of a book
Nietzsche was content to have a superficial understanding of Stoicism - or at least was content to mischaracterize it. The Stoics have much to say of their view of nature - and much of it I discard without the intelligent design component. But that doesn't change that Nietzsche cannot honestly substitute his view of nature for the Stoics and fairly criticize them for the contradictions that arise.
Part of the beauty of the Stoic philosophy is that it's far more forgiving than Nietzsche. Marcus also learned from Rusticus:
> with respect to those who have offended me by words, or done me wrong, to be easily disposed to be pacified and reconciled, as soon as they have shown a readiness to be reconciled
Marcus wouldn't mind Nietzsche's criticisms very much.
Edited for formatting