Can SQL Server start taking backups by itself?
Most likely it is a 3rd party backup solution such as NetBackup that your sysadmins have pointed to your instance.

Try reading the default trace to see if the application name column gives you the specifics:

-- read all available traces.
-- including current
DECLARE @current VARCHAR(500);
DECLARE @start VARCHAR(500);
DECLARE @indx INT;

SELECT @current = path
FROM sys.traces
WHERE is_default = 1;

--remove the rollover number from the filename 
--(i.e., log_157.trc becomes log.trc)
SET @current = REVERSE(@current)
SELECT @indx = PATINDEX('%\%', @current)
SET @current = REVERSE(@current)
SET @start = LEFT(@current, LEN(@current) - @indx) + '\log.trc';

-- CHANGE FILTER AS NEEDED
SELECT 
    TextData,
    ApplicationName, 
    StartTime,
    CASE EventClass
        WHEN 46 THEN 'Object:Created'
        WHEN 47 THEN 'Object:Deleted'
        WHEN 164 THEN 'Object:Altered'
        ELSE 'Other'
    END as EventClass, 
    DatabaseName, 
    ObjectName,
    ObjectType, -- https://msdn.microsoft.com/en-us/library/ms180953.aspx
    HostName, 
    LoginName
FROM
    ::fn_trace_gettable(@start, DEFAULT)
WHERE 1=1
    AND DatabaseID &lt;&gt; 2 --eliminate tempdb
    AND DatabaseName = 'model'--Like '%master%'
    AND Textdata like 'Backup Database%'
ORDER BY StartTime DESC