Pardon intrusion ...
The settings for automated backups show 'course backup area' which is moodledata/filedir/
So it could be the ownerships/permissions on all of moodledata ... not the code directory ... is the issue. Your apache error logs would probably have references to not being able to write to some directory in moodledata/filedir/
How did you find those 20kb .mbz files? The backup process actually stores those files in /moodledata/filedir/##/##/somelongcontenthashname ... which is humanly un-recognizable ... ie, file doesn't have a .mbz extension at all.
IF you were using DB queries of mdl_files and saw a reference to a backup file and file name that's meta-data in the DB itself ... not really the physical file in /moodledata/filedir/ So to see if there is a .mbz file in /moodledata/filedir on has to use the contenthash info which shows a long value consisting of a bunch of letters/numbers.
The first two characters of contenthash is a subdirectory in moodledata/filedir/
The second two characters of contenthash is a subdirectory or the subdirectory above
and finally, in there the file has the name of the contenthash.
'spirit of sharing', Ken