Thanks for the link.
On a page other than the one you linked, it says, “Although the patient has a dead brain and dead brain stem, there may be spinal cord reflexes that can be elicited (a knee jerk, for example). In some brain dead patients, when the hand or foot is touched in a particular manner, the touch will elicit a short reflex movement.”
I wonder if that is what the mother observed when she says that her daughter responds to touch.
These people need a good chaplain to talk to them and encourage them to accept the reality. Prolonging the time the body is kept on a respiratory and keeping their false hopes up is just going to make the crash that much harder when the body inevitably fails completely.
It is called the Lazarus effect or sign.