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.
BTW, there's still an effort to recruit foreign born medical personnel to this country but it's being interfered with by the folks who'd rather have more Mexicans to mow their lawns.
The visas needed for the doctors and nurses disappeared last year in the remains of that Comprehensive Immigration bill.