MediaWiki works fine on shared hosting, but there is (at least) on catch. When uploading files, MediaWiki, by default, saves a lock file in the /tmp folder without randomizing the file name. This will cause a conflict with multiple installations on the same server.
As a solution, we you must add the following line to the LocalSettings.php file:
$wgTmpDirectory = '/home/UserName/private/tmp';
where UserName is the Linux username of your account (on CiviHosting servers, this is the main Control Panel login as well). Then the upload wizard works fine.