Gwatkin said she frantically pulled the bands from the child's neck, picked her up and took her home.
"I broke down and cried, not knowing what would have happened if I didn't get there when I did," she said.
She claimed a teacher was beside Addison and didn't notice.
Addison had been in hospital two weeks before the incident after an asthma attack. Gwatkin laid a complaint with the Ministry of Education about the daycare, which is owned by national chain Kidicorp.
Kidicorp chief executive Fiona Hughes said an internal investigation found Addison had been playing with a board game in which rubber bands were wrapped around pegs. A staff member had changed her nappy five minutes before Gwatkin arrived.
In that time, she had wrapped the rubber bands around her neck.
"We were satisfied that the child wasn't having difficulty breathing, wasn't distressed. However, it's not ideal to have a game where there is potential for harm," said Hughes.
"[Gwatkin] was assuming that this could have caused some problems, and it certainly could have, but the rubber bands are quite large and there are no indentations on the child's neck."
Hughes told the Herald on Sunday yesterday the Education Ministry was "satisfied" with the internal investigation.
But, Katrina Casey, head of sector enablement and support, said the ministry was still investigating.
"We are always concerned when we hear claims that a child's safety has been put at risk," she said.
"If a complaint has been made to us we will investigate ... to establish the facts and ensure processes are in place that will minimise the risk of similar incidents happening again."
