You forgot to note that INSERT/EXEC cannot be nested. If the procedure does internally the same trick, you won't be able to insert the results into a table.
One possible solution is setting up a "SELF" linked server, pointing to the instance itself, then querying the procedure with something like:
SELECT * INTO #SomeTempTable FROM OPENQUERY(SELF,'EXEC myDB.dbo.MyProcedure')
-- Gianluca Sartori