-- When ASP.NET AJAX Beta1 is copied into the GAC of a server, it can be used in partial/medium trust just fine by any application on it. So if your hoster has installed ASP.NET AJAX Beta1 on a remote system, you are set -- it will work fine in medium trust.
The problems in the above thread occur when your hoster hasn't installed ASP.NET AJAX Beta1 onto a system yet. Because of the way the Beta1 assembly is marked, it doesn't support simply copying into the \bin directory and having it work in partial trust. It has to be installed in the GAC of the system to support medium trust.
We are working hard with hosters to get them to install the ASP.NET AJAX Beta bits on their systems (meaning to add it to the GAC). Because this is a non-impactful install (it can't screw up anything on the machine), it is a very safe thing to-do and shouldn't cause any problems to any application. Once they install it, then you can simply copy your apps up to the remote system without any problems and have them run in partial trust.