When I go to [url]/api (where [url] is the url of my Magento), I get this response:
I'm late but hope my reply will be useful for someone in future.
I had exactly the same problem. I had installed Zend Server (PHP 5.3.9) and was getting the same error. I searched a lot and applied all available solutions but fails.... Finally, i installed wamp and then run 'Soap Client' script over there and it runs successfully.
Then i reached on this point that Zend Server (PHP 5.3.9) has some default bug in 'Soap Client' Script. I uninstalled Zend Server (PHP 5.3.9) and installed Zend Server (PHP 5.4.11) and runs 'Soap Client' script over there. This time it runs successfully.
Conclusion: Please use latest PHP version (Zend Server) or (Wamp Server) as, there is default 'Soap Client' bug in some PHP versions, one i mentioned above.
Thanks, Kashif
The answer is: it comes from a PHP bug. The truth is in a post by floriancarstens here: Magento Forum