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The “Reported By Anyone” option actually combines these 4 aspects:
Tickets that are reported by you
Tickets where you are a participant
Tickets that are shared with you
Tickets that are shared with organizations you are in. Unless you are the admin user as admins see all organizations.
This option DOES NOT show all tickets in general, it only shows all tickets that you are supposed to see in your Service Desk report. This means that even if two users are in the same organization, it’s possible that one of the users doesn’t see a specific ticket because this ticket is still not shared with any organization.
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You’re an admin user
You have project permissions that allow you to see more tickets
The Advanced Reports configuration of the project has the option “Show all requests in the report.” enabled. (WARNING) This overrides every other option and shows all tickets, you should be careful when enabling it.