On 11th of March Google has announced significant extensions of their API which will allow developers to create even more integrated mashup experiences.
I haven't spent a great amount of time in investigating the issue but it currently seems as if YouTube's web servers do not allow cross-domain access, so trying to e.g. execute a ClientLogin() request against the YouTube API results into a security violation exception being raised. They obviously do also not support Flash/Flex based cross-domain access, as Silverlight 2.0 also respects the cross domain authorization for Flash players and would work just fine.
I've sent the Google API team an email about it and wait for an answer.
Part 2 of my tutorial on HTTP networking with Silverlight 2.0 will then showcase how to build an integrated experience with Silverlight and the YouTube backend!