My two pennies:
When my now wife was going through the process to get her green card. There were lots of questions that seem silly. Were you ever a prostitute? Are you working for a foreign govt? And the such. The reason for all these question is that if they find out that you were , you would then lose your Green Card. And if you got citizenship, you might lose that too.
There were some nazi prison guards that have been in the USA as citizens for decades that lost that citizenship because they had been deemed to have lied on the green card application.
So yes, you could lose your US citizenship too if you lied on your green card ap, and citizenship ap.
If the viet woman married a taiwanese person and quite soon got into an affair with someone else, and she lost her citizenship. I think that is not incorrect. She got the citizenship through marriage and now she divorced?
I think if she divorced the man, then it stands to reason her original reason for marriage is invalid.
Unless the marriage had gone on for many years already, but if she just married and then divorced in a short time frame, it stands to reason she may lose her citizenship by marriage.
The US has some good provisions for Green Card holders though. Once they have their green cards, they can divorce (after two years) and still retain their green card. Or if they can show spousal battery they can still apply for 10 year green card even if they divorce before the two year initial green card expiry.
That is a protection of civil rights.
But I would imagine if a foreigner married an American and got a green card and then had a child with someone else and was facing divorce, chances are she will lose her two year initial green card status.
But once a citizen, it would be unlikely. As the citizenship process takes a good many years.
Once a citizen it would take something more major, like being guilty of mass murder or some such in his/her former country, etc.