IME, the current 'thing' is to keep the children with the parents if at all possible.
Children can be removed from parents at birth, but not on a whim.
There will either have been parallel planning during the pregnancy - i.e. an action plan which would have enabled the parents to keep the baby and a plan B in case they failed to follow it.
A single plan of removal at birth, on the basis of prior knowledge of the family.
A change in circumstances which meant that the parents are not able to look after the baby.
Or thereabouts.
Whatever happens, SWs are not able to swoop in and remove children. They have to compile evidence, write reports and present these at court. Courts make the decisions to remove children, not SS.
I wouldn't necessarily believe her, but I would still feel sympathy (to an extent). Few people don't care that their children have been removed, they just don't understand why they need to do what they need to do to keep them and are unable to parent appropriately.
If she did have her baby removed because she is morbidly obese, it will be because she, in her unique position, posed a risk to the baby.