I didn't get the sense that her parents were involved. And it doesn't sound at all unlikely to me that an adoption agency told her it wouldn't take a biracial baby. Many adoption agencies (then and now) aren't affiliated with any orphanage, and only take a baby off a birth mother's hands when they have an adoptive home for it. With healthy white infants, there is never a problem lining up adoptive parents well before the birth (though it was probably hardly a few decades ago, when few women put off child-bearing until their later 30s or early 40s, and so infertility was much less common). An agency not affiliated with an orphanage or similar institution would have no place to put a baby that it couldn't immediately find a home for, and would most likely simply tell the mother to turn it over to a state child welfare agency, since that's all the adoption agency would be able to do with it.
It was illegal then and now for an adoption agency to reject a child on the basis of race. She is lying.