These are not only Witch’s words. If I recall well, Mr Beaver said that Edmund betrayed his siblings and joined the Witch when they first appeared in Aslan’s camp.
But anyway, I stand in a position, that Edmund’s betrayal wasn’t known in the country afterwards. Few reasons:
- as already mentioned, Aslan said there’s no need to talk more about it; anyone who would elaborate on this subject would go against Aslan’s straight wish; I don’t suppose that creatures which were in the camp then would be willing to do so;
- the treason was in fact against his siblings, not Narnians; so it was for them to decide whether to keep resentment against Edmund or not;
- also mentioned – just afterwards Edmund was fighting against Witch, side by side with those creatures, which were earlier in Aslan’s camp; and he was nearly killed when doing so;
- then he was made a king by Aslan himself.
How many of veterans from Beruna would be willing to spread rumores about Edmund being a traitor? Especially that none of them new precisely what happened. And even if there would be someone to speak about it, he would have grave difficulties with finding someone to listen. Just try to immagine such a situation (we’re talking about a newly appointed, long awaited king):
„You know what? He was a traitor. He...”
„How dare you?! One word more and I’ll send for guards to arrest you for laesa maiestas!”
End of conversation.

Krystyna