First, the original sentence should be :

Alors c’est vous, ces braves [que] l’on m’a dit être attirés par notre mouvement de libération ?

The “que” here is required for the meaning, I think you wanted to emphased it.

The 2 layers should be 3 :

• Ces braves sont attirés par notre mouvement de libération. (the information)
• On m’a dit que ces braves le sont. (the source)
• Alors c’est vous, les braves dont on m’a parlé ? (the question)

Why “que” has been chosen ? Wiki answers :

Conjunction

que

1. that (introduces a noun clause and connects it to its parent clause)

And moreover, the layout 2 is the keystone of the two others.

You cannot say "ces braves que l’on m’a dit", here we can use que only because of the adjective : "attirés" (present participle used as adjective).

You can see the same construction with "penser","imaginer",… :

Ces gens, qu’on imagine braves et courageux, sont simplement animés par la liberté et n’ont pas d’autre choix

Les politiciens que l’on dit corrompus et animés par l’argent finissent quand même au deuxième tour des élections

"Que l’on m’a dit [adj] " is a slightly more complicated construction but it’s the same idea.

(By the way I wasn’t sure so I looked it up, you can say "pas d’autre" or "pas d’autres", it depends on what you want to imply)

“Brave” is here used as a noun, not as an adjective.

In addition, if people were attracted by this movement, the narrator would have said “ces braves qui sont attirés par…”. But the narrator was told that these people are attracted; for this reason, the structure of the sentence is different.

I would say that in this specific example, the usage of “que” vs. “qui” is not a grammar issue; this is rather a different construction because the meaning of the sentence is different.