This isn't to say that you can't Declare a Story Detail in Fate Accelerated Edition. You could. See Can players spend Fate points to introduce story details in FAE?
But can you use Create Advantage to create a story detail in FAE?
Aspects are true. By Creating an Advantage, you can create a new Aspect. That Aspect is a "story detail" in the basic sense - it's a detail of your story, and you brought it in to the story via in-character actions (your character's own effort).
This isn't the same thing as the "Declare a Story Detail" rule on page 13 of Fate Core. For that, you aren't using the Create Advantage action and you aren't creating an Aspect either: You, out of character, are simply spending a Fate point to get the GM and the rest of the table to agree to a story detail you want to introduce. Your character might act on this fact after the rule is exercised, but the rule doesn't involve the character's own effort.
So? Yes, the use of the Create Advantage action can create narrative information which wasn't there before (the acting character makes something new true). But, No, it's not the same as Declaring a Story Detail (the player makes something new true).
Where you (and the FAE book) talk about how "Aspects establish facts", understand that in Fate, not every true fact is an Aspect. This is how a "story detail" is used: Something can be true and therefore allow certain character actions, but, it's not something which can be invoked without an additional create-advantage action.
I'll illustrate both of those ideas using the example from Fate Core:
An adventuring party encounters a village where the inhabitants are speaking some random language which none of the players have been established to know. One player has a studious academic type character, with the Aspect "If I Haven't Been There, I've Read About It" and wants to use the Declare a Story Detail rule to establish that they are familiar enough with that language to be able to communicate.
At this point, this player isn't Creating Advantage (nor her character). For Create Advantage to be of use here, the player would describe some effort her character is undertaking, in order to create a result. At this point, the player is simply spending a Fate point to justify being able to communicate.
Great. The party now has a character who can talk to the inhabitants of this village. Now that they're talking, NOW they can use the Create Advantage action to try to do something which they couldn't have done at all if they couldn't communicate with the village. What if the adventurers know that some attacking horde is about to descend upon the hapless village, and they want to rally the villagers to defend themselves more effectively? They can now (since they can converse) do things like using Create Advantage to Carefully explain the threat, making the villagers **Fore-Warned and Fore-Armed". Or they can use Create Advantage to Flashily inspire the villagers' morale and confidence: "Lifted Spirits, Bolstered Will".
You see how it's two different things. Both activities can make new things true in the story.
Declaring a Story Detail is an out-of-character activity, costs a Fate point, and doesn't create an Aspect (but should be justified by relating to an Aspect already present, according to the rule text).
Create Advantage is an in-character activity, doesn't cost a Fate point, and (usually) creates a new Aspect (or lets a "hidden" one be discovered, or puts free invokes on Aspects which are already present).
Last thought: Even though this "rule" and this use of a Fate point isn't described in the FAE text, there's no reason it couldn't be included in your game, if someone wanted to. The way it would come out in play might be, like, one of your players is in a situation and says something like, "Well, we've never specifically talked about whether my guy is immune to iocaine powder or not, but, as an Intelligence Corps Diplomatic Operative who has been carefully Prepared for All Contingencies, wouldn't it make sense that I could handle the substance without ill effects?" GM: extends hand to receive Fate point "Maybe it would! How bad do you want it?" If the player doesn't want to just "make it so" with a Fate point, she could still just roll to Overcome the danger of handling the poison.
Be sure to go ahead and read how Declaring a Story Detail works in Fate Core (link).