File.Copy results in Access to path '' is denied.

I am using an intranet web form app and am trying to copy a file from one machine to another using UNC paths. For this example, lets say the syntax of the failure is:
File.Copy("\\Server1\folder1\abc.pdf", "\\Server2\folder2\abc.pdf") results in: Access to path '<PATH\FILE>' is denied.
As a reference File.Copy("\\Webserver\folder3\abc.pdf", "\\Server2\folder2\abc.pdf") does not throw an error.
Some info that I think is relevant:
Server 1 is a Windows 2012 64 bit machine. Server 2 is a Windows 2000 32 bit machine. Web server is a Windows 2003 64 bit, II6, Framework 2.0.50727, DefaultAppPool The site's web.config is set for <authentication mode="Windows"> and <deny users="?" />. IIS is configured for no Anonymous access and Integrated Windows Authentication. The following users have been added for the secu ...