First, the author fed an unpublished draft to Anthropic's hosted model. I assume they did this from their personal account, that may include a credit card or at the very least a pseudonymous name that is uniquely identifiable.
Then, the author fed an unpublished draft to Anthropic's hosted model, except in Incognito or whatever. We are led to assume that, whatever the author did for the second submission, they did so in a way so that Anthropic could not correlate both distinct requests from one another. Perhaps on a second subscription? They don't say. I am highly skeptical they airgapped their requests properly so that it doesn't look like the same user is making the request to the same hosted model.
Then, the author asked a friend to publish the draft. A friend, of which there is probably a digital trail that maps the relationship of the author to their friend.
All of this metadata could be crunched on the backend before the black box spits out a response.
Across all these datapoints, I have high confidence a model of this caliber could put two and two together and determine that the author penned the drafts, not solely because of stylometry, but because there is a clear behavioral pattern tying all three events together.
An assumption made here is that Anthropic doesn't train on chats. Though the author opted out of training on their chats, and session memory, how could you trust a hosted model to respect such opt outs?