There’s no sign of Professor Gibson saying that. She does seem to have said the child was:
as safe in hospital as she would be outside.
and that allegedly, in the words of the BBC reporter (no actual words offered):
the best plan was to send her daughter to complete her treatment in Dumfries, where the family lived.
What we have here, as in all of the recent BBC Scotland reporting on the hospitals inquiry, is the regular use of speech marks, based on the words of parents, to manufacture headlines worthy only of the National Enquirer (like the Sun but worse)
Sturgeon ate my daughter’s hamster?