I think you misunderstood the attack. The idea behind the attack is that the attacker would create what is effectively a honey pot website, which writer.com customers want to use as a source for some reason (maybe you're providing a bog-standard currency conversion website or something).
Once that happens, the next time the LLM actually tries to use that website (via an HTTP request), the page it requests has a hidden prompt injection at the bottom (which the LLM sees because it is reading text/html directly, but the user does not because CSS or w/e is being applied).
The prompt injection then causes the LLM to make an additional HTTP request, this time sending a header that contains the customers private document data.
It's not a zero-day, but it is certainly a very real attack vector that should be addressed.