One of the things to look for in forums is date of the thread. The first posting in this thread was back in 2011. Some information provided in this thread applied back then. However, Moodle has moved forward and changes were made so some postings may not apply now. Around version 2.6 an 'experimental' compression showed up ... a .mbz (which used to mean 'moodle backup zip') was no longer accurate IF one turned on and used the 'experimental' tar.gz compression. Moodle's extension for a backup did not change.
Fast forward to version 2.9 .... the latest and greatest as of the date of this posting. The default compression is now tar.gz. Extension to backups are still .mbz, however.
Changing file name extensions, BTW, is a step primarily for users who use systems that rely upon those three letter extensions to determine what applications are associated when one clicks/double-clicks on them. On Linux (MacOSX), if one were to know the file stored in filedir/x/y/[bunch of letters numbers] was a tar.gz, one doesn't need to change the filename to include an extension to be able to use tar zxvf [longfilename].
It should be noted, somewhere, that one may not remember what compression routine was in use when a backup was made and before one attempts unzip/tar zxvf an inspection of the file properties itself would help to know. A file -b [file].mbz, however, will report it's a Zip and one must have version 2 to unzip on a Mac - even though it's a tar.gz. When trying unzip on a .mbz that is a tar.gz it will error out. When that happens, try the other! ;)
But, you've worked through your problem and that's good! Congrats.
'spirit of sharing', Ken