Michelle's parents were presumably lawful entrants with a family "student visa". The law at that time, and now, requires that when a baby is born he or she must be added to the family visa.
US citizens are not, of course, required to have a visa to enter or stay in the country.
There's a discontinuity in the law and the fair way to deal with it is to simply return all persons required to be entered on a family visa to their native country to make an application for immigration ~ like everybody else.
Wouldn't bother me a bit to help Michelle board the plane home eh!
In the 1960’s-70’s, the United States recruited a large number of physicians and other health care professionals from the Philippines, with the intent that many of them would stay in the US. You say that her parents came here on a student visa. I don’t know if that is true or not, but US immigration policy has different kinds of work visas. Some of the workers are supposed to be temporary, and some will clearly become permanent residents.
Since we don’t have any proof one way or the other what kind of visa they had, it seems pointless to speculate. I think it’s preposterous to say that a medical student at that time would not have obtained legal status without having a baby here.