[RPG] Do advantages in Fate Core just “wear off?”

I don't have my books handy, so I can't quote rules for you, but here's my recollection based on several years of playing Fate:

Players can narrate their own actions. And they can answer questions that you ask them - filling in blanks and taking a portion of the burden of narration from you.

But when they want to create facts to their own advantage, they usually have to earn it. Earning it means succeeding in rolls or spending Fate points or sometimes both.

For example, if a player wants to to put the aspect On fire on something, she can't just make it so by saying so. She has to Maneuver Create an Advantage.

If a player wants to change an existing fact, that has to be earned, too, if it's important. The simplest example is this: A door is locked shut. The player wants it open. To make the open door a fact, she'll have to pick the lock with a roll, get the key with a roll, or bash it down with a roll. You and your players have an intuitive understanding that this is so.

Aspects can create facts for players, but they have to be powered by a Fate point. For example, I can say, "I'm invoking Better late than never to put myself in the scene now!" presuming I have an aspect "Better late than never" and the action has already started (so that I'm late) and also assuming I pay a Fate point for it. But the GM can give me a Fate point to cancel that invocation.

Your player created a fact out of nothing - he got to narrate how he succeeded at his roll, but since everyone's job is to make everyone else look awesome and his narration is squashing your awesome with "meh", you are fully within your rights to veto it.

Here's the only thing I would have done differently and would suggest that you do differently too:

As you say, "nah, sorry, but that didn't happen", hand over a Fate point. You are saying, silently, but concretely, "I am taking over narration here. Sorry, but in exchange, I am literally handing over narrative power that you can use later."

You're gonna have to go to the Fate Core book for the full explanation. Although they don't mention it for this particular case, FAE makes a habit of expecting players to refer to Core for more details on a host of subjects. This is because Fate Accelerated, in order to stay svelte, doesn't talk much about corner cases. Since multiple free invokes on one aspect usually come from "with style" outcomes on Create Advantage, that's where they put this detail. They may feel it's implied on page 28, but it could definitely use more explication.

So for more comprehensive coverage we look at page 70 of the Fate Core book, Free Invocations:

Free invocations work like normal ones except in two ways: no fate points are exchanged, and you can stack them with a normal invocation for a better bonus. [...] You can also stack multiple free invocations together.

It's a shame they left these lines out of Fate Accelerated, but comparing the two books' phrasing we can easily infer that they had this rule in mind. They just pared it down a little too aggressively.

So the answer is: Free invokes, as part of their inherent "freebie" nature, ignore the "one invoke per aspect per roll" rule, stacking with each other and with normal invokes. Put another way, you can invoke an aspect as many times as you like for the same roll provided a maximum of one of those invokes is made using an actual factual Fate point.

This means you can stack one normal invoke (powered by a Fate point) with as many free invokes as you have available on the same aspect and get the full effect of all of them.