Cannot access prestashop 1.5 web service

I have a demo prestashop installation with webservices enabled, but I cannot access them. I looked around and there was an incompatibility with php running as cgi, but it's solved in 1.5. Of course credentials are ok (I have tried regenerating the access token).

The only hint I have is that prestashop complains about mod_rewrite not being enabled, although it actually works.

The api url is http://www.yourapp.it/presta_demo/api/ and the access token is 0ITOMIGPZGB2JQXO0SNM1GL1E3PP5EAP You can try freely, it's a demo instance.

I have enabled php cgi mode in prestashop webservice settings. This is my .htaccess:

# ~~start~~ Do not remove this comment, Prestashop will keep automatically the code outside this comment when .htaccess will be generated again
# .htaccess automaticaly generated by PrestaShop e-commerce open-source solution
# http://www.prestashop.com - http://www.prestashop.com/forums

SetEnv HTTP_MOD_REWRITE On
RewriteEngine on
RewriteBase /presta_demo
RewriteCond %{HTTP:Authorization} ^(.*)
RewriteRule ^(.*) - [E=HTTP_AUTHORIZATION:%1]

RewriteCond %{HTTP_HOST} ^www.yourapp.it$
RewriteRule . - [E=REWRITEBASE:/presta_demo/]
RewriteRule ^api/?(.*)$ %{ENV:REWRITEBASE}webservice/dispatcher.php?url=$1 [QSA,L]

# AlphaImageLoader for IE and fancybox
RewriteCond %{HTTP_HOST} ^www.yourapp.it$
RewriteRule ^images_ie/?([^/]+)\.(jpe?g|png|gif)$ js/jquery/plugins/fancybox/images/$1.$2 [L]

#If rewrite mod isn't enabled
ErrorDocument 404 /presta_demo/index.php?controller=404

# ~~end~~ Do not remove this comment, Prestashop will keep automatically the code outside this comment when .htaccess will be generated again