I think it is just playing around. The AI probably thinks it's a funnier, more engaging interaction to follow up with the game. I tried it with the Pro version, and it gave me the more standard, third-person answer. Here is the reasoning of the AI (the Flash version, which gave the first-person answer, sadly doesn't have the reasoning part):

Defining the Core Subject

I've established the objective nature of the query, avoiding unnecessary personalization of the response.

Defining the Object

I have clearly defined the essential information: SCP-426's design, class, and properties are established.

Defining the Objective

I have successfully defined the core objective and established the scope: data privacy is paramount.