The problem seems to come from a simple oneliner: in index_rest.php, line 20:

eZSys::init( 'index.php', $ini->variable( 'SiteAccessSettings', 'ForceVirtualHost' ) == 'true' );

should be

eZSys::init( 'index_rest.php', $ini->variable( 'SiteAccessSettings', 'ForceVirtualHost' ) == 'true' );

After doing this change, accessing an url like the following:

http://localhost/ezp/installs/ezpublish-4.5.0-ent/index_rest.php/admin_site/api/ezp
/1/content/nodes/2

seems to be working with the admin_site siteaccess activated (eg. the cookie name used for the session changes)