At an inquest into Sophie's death held in Huntingdon in December, coroner David Morris recorded a narrative verdict.
The inquest heard the tree was examined prior to the incident and if recommendations had been implemented, the tree would have been made smaller, greatly reducing the risk.
It was found 11 trees in Middletons Road recreation ground were found to be a "high risk" hazard that required immediate removal and a further 18 were found with defects also requiring immediate treatment.
"Sophie's parents are still struggling to come to terms with the fact that their daughter would still be here today if these checks had been carried out."
Today the family's solicitors, Irwin Mitchell, said the family had reached an undisclosed out-of-court settlement with Yaxley Parish Council which was responsible for the tree.
Parents Laura and Martin Howard, from Yaxley, said:
The last 16 months have been horrendous as we've struggled to come to terms with the fact Sophie is no longer with us.
She was a beautiful girl with her whole life ahead of her but this has been taken from her and it is heartbreaking. Her loss to us is immeasurable, and our grief endless.
At first it seemed a tragic case of fate or wrong time, wrong place, sadly after the coroner's inquest it became apparent that this was not the case.
We were horrified when we heard the Health and Safety Executive's report found that Yaxley Parish Council was not following the health and safety guidelines for risk assessments and maintenance in public places and that almost 30 other trees were in a hazardous condition.
We just hope councils across the country take note and learn from the mistakes that led to Sophie's death.