Had been in contact with him late June early July. He was stepping through upgrading via git. Git deals with the code directory/DB and the only way to get a current moodle code directory under 'git' is via command line. This to say he was probably logged on as root user when working on it.
The upgrade via git doesn't touch (shouldn't touch) the moodledata directory, but he may have reset ownerships/permissons on the moodledata directory for some reason. moodledata on a typical CentOS server has pretty liberal ownerships and permissions on it and all directories/files contained there in (which would include the temp/backup directory and files. Sounds now like code can't create that log file in moodledata/temp/backup/ ... which would be the first step in backing up or even restoring ... thus can't read it.
Do you have a backup of some sort you could attempt to restore ... a tinker/small course would do ... just testing restore and if successful would be removing it anyway.
chown apache:apache /pathto/moodledata -R
chmod ugo+rw /pathto/moodledata -R
will take care of that.
Of course, without seeing actual apache logs (error, etc.) above is an 'educated guess'.
Sent you a PM ... please check and respond there.
'spirit of sharing', Ken