How widely known were the pieces of text? Are we talking about a section of MLK's I Have a Dream speech or hand written birthday cards from your grandma?
I'm using those as the two extremes, but if it's anything by anyone moderately well known (even a lesser known piece of writing), I'm not too surprised that it didn't need the web to figure it out. It's like if you showed me a Wes Anderson film or played me a Bob Dylan song I'd never seen/heard before, I could probably still figure out who it is without looking anything up. I don't think it's surprising that an LLM can do that much better than a human can.
Now, if you're giving it things like personal emails between you and your family and it's able to guess who you are, that's much, much scarier.
I mean I tried sending the pieces of text to Opus that Kelsey was referring to on her blog just to independently check the identification claim. Presumably those pieces of text first appeared on the web when the blog post was published a week ago, so no model should have memorized the exact text yet. My prompt had to specify no web search, otherwise Opus would try to search the web, though it didn't seem like Opus could find that blog post even when it did try to search the web.