The toddler was killed by her mother's boyfriend in Fife in 2014. An official review into her death concluded it could not have been anticipated.
But the BBC found that a social worker had failed to warn Madison's mother about her new boyfriend's violent past.
The council said the review had found key information had not been shared.
Criticism of the council by Madison's mother and grandparents featured in a BBC documentary, Fife's Child Killings - The Untold Story.
The programme examined three child deaths in Fife within a four-month period in 2014 - Madison Horn, Liam Fee and Mikaeel Kular.
In light of the BBC's investigation, Neale Hanvey, a former councillor and former SNP lead on social work in Fife, is now calling for an independent review to "understand what happened".
Madison was murdered by her mother's new boyfriend Kevin Park at her home in Kelty, in April 2014.
During his trial for her murder, the court heard Park had 38 previous convictions, including for domestic abuse and other types of violence.
Park was babysitting the toddler when he attacked her, beating her with a pool cue and slamming her head against a wall.