Not if both parents were embassy staff. The 14th amendment is supposed to exclude persons born in the United States who are foreigners, aliens, who belong to the families of ambassadors or foreign ministers. However, if the mother was a US citizen, then the baby is also.
I’m not an expert on the subject. According to the young woman both parents were Soviet citizens. She was born in a US hospital. Therefore, she retains dual citizenship.
Citizenship details are worked out in Status of Forces Agreements between sovereign nations—they are usually reciprocal.
I cannot speak for what was agreed upon by the old USSR and USA. But, in W. Germany (and I expect it also applies to the new united Germany), a foreign national born in either country held that country’s citizensship as well as that of his/her parents.
I would bet money that our arrangement with Germany was and is pretty much standard among all the nations with which we maintained diplomatic relations.