I had never tried it but I get the same results--invalid column name 'server' Which is interesting as I can do SELECT TOP 1 * FROM server.db.schema.table no problem so it's not a question of whether I can use the database remotely. I then repeated with calling a table value function on a different server SELECT * FROM Server.DB.Schema.TableValueFunction('2008-01-01') and it failed out with Remote table-valued function calls are not allowed. Makes me wish I had an aggregate function to see what error message it returns when it's invoked remotely.
Executing a stored procedure through a remote server works just fine. Interesting, interesting, I'll have to check BOL over lunch to see if I can understand why it is so.