This is the core of our immigrant problem with Mexico. If they get momma over the border to have her baby she's set... Because the baby is a US citizen so his/her parent gets a pass to be In the country.
At best, this helps the child's future opportunities, which may help the family. It in no way gives the parents a pass. A cursory review of sponsorship laws would reveal this. Yet for some reason, people parrot this silly saying as if it was somehow true.