Social workers have failed to prove that three children who suffered a variety of injuries were abused by their parents.
A High Court judge refused to grant care orders to a local authority which raised concerns about the safety of the youngsters – two boys and a girl aged between 13 months and two years.
Mr Justice Baker said the couple – who cannot be identified but are in their 30s and come from Devon – were "simply dotty" about their children.
He said it would be "surprising" if "such parents" could have inflicted injuries and suggested that the causes could be medical or accidental.
The judge published his decision in a written ruling after hearings in the Family Division of the High Court in Exeter.
Mr Justice Baker said medics at the Royal Devon and Exeter Hospital in Exeter had alerted authorities in the summer of 2011.
The judge said the alarm was raised after the girl – born in February 2011 – collapsed and was then found to have a subdural haemorrhage and fractures.
Her brother was then found to have subdural haemorrhages and nine rib fractures.
Investigations began and the children went to live with grandparents, the judge said.
The younger boy was born in April 2012 and placed in the joint care of his parents and grandparents as part of a written agreement with social workers.
Less than a month later he was admitted to hospital with skull fractures and a subdural haemorrhage, said the judge.
Following that incident local authority bosses had begun legal action with a view to removing all three children from the care of the family.
Mr Justice Baker said an ''important feature" of the case was that each parent suffered from a ''range of medical conditions'' and that the family's medical history was ''complex".
The judge said it could not be known which "unusual" medical features and conditions had been transferred to children and had "an impact on bone fragility".
He said the father's "most troublesome ailment" was kidney stones, which were associated with imbalance of calcium and other minerals. He said one of the children also had a kidney problem. And the judge said there was a "possible association" between calcium imbalance and reduced bone density.
Mr Justice Baker said another "striking feature" was a lack of external signs of injury. He said the children had been "seen very frequently" at home by a range of health workers and been regularly examined by a very experienced health visitor. But he said "not a single bruise or mark" which suggested a fracture was seen.
He said the children's mother and grandmother had told how the youngest child was hurt when he accidentally fell from a Moses basket onto a wooden floor – an account he accepted. He said medical evidence was "consistent" that explanation.
And he said apart from the injuries there was not a "scintilla of criticism" of the way the couple had cared for the children.
"My impression is that the longer this process has gone on, the greater the degree of uncertainty. Gradually the inquiry unearthed a number of unusual features," said Mr Justice Baker.
"The picture that emerges ... is that these are doting parents who are devoted to the children and provide them with a very high level of care."
He said the local authority – Devon County Council – could be named but neither the children nor members of their family should be identified.