When I joined a view which takes input from another view and then published it as web service, I was able to browse the web service without providing any input parameter. It took the input from the second view and provided me with results.
I would check if the web service is built over the finally constructed derived view. If the web service is built on top of the view which requires an input to run, then it would look for that input when it runs as a web service as well.
Hope this helps!