Strange Backup and Alerting Issue
You can get an idea of what backups have been taken, and when, by looking at the result of this query:

DECLARE @DBName SYSNAME;
SET @DBName = DB_NAME(); -- modify these as you desire.
SET @DBName = NULL; -- comment this line if you want to limit the displayed history

SELECT DatabaseName = bs.database_name
    , BackupStartDate = bs.backup_start_date
    , CompressedBackupSize = bs.compressed_backup_size
    , ExpirationDate = bs.expiration_date
    , BackupSetName = bs.name
    , RecoveryModel = bs.recovery_model
    , ServerName = bs.server_name
    , BackupType = 
        CASE bs.type 
            WHEN 'D' THEN 'Database' 
            WHEN 'L' THEN 'Log' 
            ELSE '[unknown]' 
        END
    , LogicalDeviceName = bmf.logical_device_name
    , PhysicalDeviceName = bmf.physical_device_name
FROM msdb.dbo.backupset bs
    INNER JOIN msdb.dbo.backupmediafamily bmf 
        ON [bs].[media_set_id] = [bmf].[media_set_id]
WHERE bs.database_name = @DBName
    OR @DBName IS NULL
ORDER BY bs.backup_start_date DESC;


By default, this will show you all backup activity that has occurred on the current instance since the last time msdb was created/restored, assuming backup history has not been deleted.