Full backup at 1am, not started by my maintenace plan
Add columns:
    msdb.dbo.backupset.software_vendor_id, 
    msdb.dbo.backupset.user_name

to your query.

If your software vendor id = 4608 then its sql native, anything else is a third party software. The user name should give you some clues as to what is occurring.

Also check SQL Agent for jobs executing at around that time.