I do apologise. It seems I can't upload a screengrab here so I'll describe what I do and get.
1) I have installed your http and oauth classes and set-up oauth_client.php and test_oauth_client.php as best I can with the data provided by the oauth and API documentation
2) I direct my browser to http://subdomain.mysite.com/api_demos/test_oauth_client.php where it is installed.
3) My browser redirects to this page:
secure.oauthserver.com/OAuth/access
...
4) and displays this JSON string:
{"access_token":"536312b0-7392-4990-ba48-f2dc7d563315","token_type":"bearer","expires_in":3600,"refresh_token":"9e0c313c-6192-4991-bcd9-2359bbea40ed"}
5) The log reads as follows:
[28-Feb-2013 10:21:01] OAuth client: Checking if OAuth access token was already retrieved from https://secure.serverdomain.com/OAuth/access_token
[28-Feb-2013 10:21:01] OAuth client: Checking the authentication state in URI /api_demos/test_oauth_client.php
[28-Feb-2013 10:21:01] OAuth client: Redirecting to OAuth Dialog https://secure.serverdomain.com/OAuth/access_token?client_id=clientid.subdomain.serverdomain.com&client_secret=6CD3B809-BEC3-4684-BFC0-26D68A816878&grant_type=client_credentials&scope=RegisterUser&redirect_uri=http%3A%2F%2Fsubdomain.clientdomain.com%2Fapi_demos%2Ftest_oauth_client.php