As a foreigner, I have never been bothered when asked where I'm originally from, in fact I know it's a 'sensitive' subject sometimes, however the way it's been asked '.. Really from..' plus asking so many times... Suggests to me that there were other motives behind the question.
I think the first issue is that the question she asked ("Where are you from?") wasn't the question she intended to ask ("Where does your ancestry lead?"). An understandable mistake in the modern society where ancestry has become seen as the be all and end all as part of the massively promoted modern belief in unchosen group identity.
Then the second issue is that she persisted in re-asking the same question and not accepting the answer because it wasn't the answer to the question she intended to ask.
I get a more regional version and also a national version on a similar scale. I'm from Stoke-on-Trent. Anyone who hears me will instantly know that I didn't grow up in Stoke-on-Trent. Where am I from? Stoke-on-Trent. It's my home. I am a Stokie. I
was from another part of England. I
am from Stoke-on-Trent. Where am I really from? Stoke-on-Trent. I'm also the first generation of my family born in England. Where am I from? England. Where was I from? England. Where am I really from? England. I am English. My heritage is that of Shakespeare and Chaucer and Alfred the Great and all that. English, all the way through. My ancestors weren't English. I am not my ancestors. I am me. It's the conflicting concepts of "a person" and "unchosen group identity" again.
The wording and persistence would irritate me. But the person in question is 83. She grew up in a different culture, a culture in which "race" was much less important than it's believed to be nowadays. She's not completely au fait with modern fashions and she missed the mark with her phrasing when trying to match up with modern fashions. I'd cut them some slack for that.
EDIT: I've just seen the photos. The clothing changes things entirely. The person was clearly dressed to state a different identity, not British. So the question becomes much more appropriate. Although still lacking in clarity and excessively persistent. But...83 years old.