What might cause tickets to automatically solve or close upon creation?
Tickets can close on creation via a specific trigger that would accomplish this task using the action Ticket Status: Closed.
To find this information, open up the ticket in question and check its audit trail (Viewing all events of a ticket). When you're viewing a ticket, you can find audit trail details by clicking the Conversation drop-down and selecting Events.
From there, you can determine which trigger fired on the ticket and updated its status.