Here's the basic problem: They gave a month deadline. That's not enough time to get permission for time off from work, book a ticket, take photos to show there is no city there, and submit, at least with the required degree of integrity (e.g. confirming GPS coordinates in some temper-proof way, etc. -- they'll just say you took the photos elsewhere). There is no city there. Pretending it's a fake conspiracy seems to…
After ~25 years of this running conspiracy if none of the evidence was collected we can call it evidence that the conspiracy theory is indeed fake.