The user ID I used to do the load is the instance owner/creator, it is also the domain administrator (not just a user) for the same domain all my db servers belong to. And the IMPORT command works just fine with the same source data files. Also, all DB2 services are started by the same domain user account.
To recap my problem:
The Import command works fine with all files regardless where they are located, but the Load command only works for files on local disks.
For example:
db2 load from X:\test.dat of del insert into edw.test
SQL2036N The path for the file or device "X:\test.dat" is not valid.
However, the following command works:
db2 import from X:\test.dat of del insert into edw.test