I don't think it'd be wise to pollute the context of every single conversation with irrelevant info, especially since patches like that won't scale at all. That really throws LLMs off, and leads to situations like one of Grok's many run-ins with white genocide.
FWIW, I did that--5 (Instant) with "(do not web search)" tacked on--and it thought the case was real:
> Based on my existing knowledge (without using the web), Varghese v. China Southern Airlines Co. is a U.S. federal court case concerning jurisdictional and procedural issues arising from an airline’s operations and an incident involving an international flight.
(it then went on to summarize the case and offer up the full opinion)
I just asked ChatGPT, Grok and Qwen the following.
"Can you tell me about the case of Varghese v. China Southern Airlines Co.?"
They all said the case is fictitious. Just some additional data to consider.