I found the explanations under the heading Prepare the directories insufficient. Since I failed to update existing Wikis, after a change of the provider, I tried to make fresh installations of MediaWiki 1.20 and failed again. Following the recommendation: "Depending on the server configuration, in some cases you have to check all boxes (777) in FileZilla, to be able to run the installer." I got the error message:
Please check and correct - File permissions to chmod 644 (for all files php, html, etc.) - Directory permissions to chmod 755 / html / * - Owner and group webX (your account - for example, web1) - Hosting Control Panel -> httpd-spezial -> mod-rewrite -> On - .htaccess file for typographical errors or incorrect commands.
This was the hint to success. On the server in question, it was chmod 755 instead of chmod 777 and for the files chmod 644. Hope, this is helpful to others.