I just realized that BULK INSERT is not supported on SQL Server Azure, so had to change some import scripts to use BCP instead. The response you get from SQL Server Azure does not explicitly tell you this. MSDN’s article on BULK INSERT does not say so either. Thanks to some kind folks at Stack Overflow for point me to BCP.
Since BCP works on a local instance of SQL Server as well as Azure, I will stick to it for now, unless proven otherwise.