One of the authority's own councillors has also voiced concern about the case and said it was now up to the council to "rubbish" the claims.
The claims were made on a British National Party website but have now been taken off after legal action brought by Neath Port Talbot Council.
It was claimed the girl was "kidnapped" by police and social workers while in hospital abroad, with her grandfather threatened at gunpoint.
She was then said to have been flown back to Britain using a false passport.
It was also claimed the youngster was diagnosed with a medical condition while overseas after doctors in this country ruled there was nothing wrong with her.
The authority took out an injunction at the High Court of Justice. It says that, for legal reasons, it can make no comment. Under the terms of the injunction, no information can be published identifying the child. At the time of the alleged incidents, she was 12.
The BNP website described her as "a lonely little girl" whose life had been turned upside down for reasons that she could not understand.
It continued: "This is a clear case of kidnapping."
It claims doctors in Britain said there was nothing wrong with her, but when she was taken abroad doctors found she had a serious medical condition.
One supporter posted a comment alleging that a false passport was obtained to snatch the child from the foreign hospital, alleging no care order or order of extradition was ever in place.
Another added: "This child was taken by police and social workers from a hospital bed."
The claims and subsequent comments have been removed from the website.
In their place is a message from site editor, retired police officer Michael Green, of Tycroes, Ammanford.
It states: "We have been silenced and are not even allowed to talk about it any more."
Coedffranc North councillor Keith Davies said: "I am not happy with the way the case has been handled.
"There is a lot of truth and substance to some of the allegations that have circulated.
"It is now for the council to address those allegations and rubbish them."