I solved the problem. It has something to do with fopen. By chance I came across a support article in my hosters knowledge base and there was explained that one can add the following 2 lines into .htaccess to make fopen work again:
php_flag "allow_url_fopen" "On"
php_flag "allow_url_include" "On"
Now package management works like a charm.
Perhaps, this helps someone.
Modx 2.1.3, PHP 5.2