Anderson picked up the Emmy for outstanding supporting actress in a drama series for her portrayal of the late UK Prime Minister - but Tanya Hart from American Urban Radio Networks was seemingly unaware that Thatcher died in 2013.
Delivering the final backstage question for Anderson, Hart said: "Just to kind of continue with the whole Margaret Thatcher thing, first question - have you talked to her about this role at all?
"And secondly, why do you think it has taken America so long to get a female leader? You know, when all of these other countries - and look at what Margaret did in the UK."
After a brief hesitation, Anderson replied: "I have not spoken to Margaret."
Then, having understandably been a bit thrown during the second half of the question, the 53-year-old stalled for a moment or two, before continuing: "Well the UK had Miss May not that long ago, which is even before the United States of America... so I think maybe the question is why is it taking the United States of America so long to get a female leader."
Well, that actually was Hart's question to be fair to her - unfortunately though, she had just bamboozled her interview subject by asking her if she'd consulted with a dead politician about her role in the Netflix drama.
So all in all, not the most productive slot with the Emmy-winner.
Still, viewers thought Anderson came out of it well, at least.
One person commented: "Full credit to Gillian Anderson for not embarrassing the reporter for not doing her homework."
Another said: "The kindest way to answer 'well, I did not consult a Ouija board as research'."
While a third added: "She is VERY kind."
The Emmy was Anderson's first in 24 years, having previously won the outstanding lead actress in a drama series award for her portrayal of Dana Scully in The X-Files.
Accepting her award, Anderson paid tribute to her manager of 20 years, Connie Freiberg, who believed in her 'when no one else would'.
The Crown was the big winner on the night, scooping a hatful of awards, including best drama series and four acting awards.