This comes from a poster named "Henry". I thought his solution was good enough, it deserved it's own entry. Here is what he said:
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I ran into this issue for attachments larger than 4KB. I solved it doing the following under IIS 6:
1. Reregister cdosys.dll
2. Run FileMon
3. Found that w3wp.exe was trying to write to Windows\temp
4. Determined from IIS Manager that the user account for the Application Pool for the specific site was "Network Service".
5. Added Network Service to Security on the folder Windows\temp folder with Modify Rights (needs delete rights or folder starts filling up with tmp files)

Problem solved.

I would like to thank this site and other posters on the web with similar issues for providing the right clues to solve this.