That's not true at all. The DACA implementation through Janet Napolitano's memo,
this one, stands on it's own. It is not connected to, nor does it need an executive order to survive.
Trump's DHS is well within it's rights to end the program. It attempted to do so through, Acting Secretary Duke's memo,
here. It cites Trump's executive order as a reason for why it is doing what it is doing, but it did not need Trump's executive order to exist and if Trump were to rescind his Executive Order No. 13,768, this action instituted by Duke would not suddenly not exist.
Because this is an independent agency action, it is reviewable under the APA, and there must be a legitimate, non-arbitrary and capricious reason behind it.
You are misstating how administrative law works when you are only talking about the executive orders here.