Actually, it is possible. I haven't done it myself, but there is a tool, DISM (Deployment Image Servicing and Management tool), that supposedly supports in-place edition upgrades, i.e. exactly what you're describing. It's talked about in Microsoft Technet at Upgrading Windows Server 2008 R2 without media - Server Core - Site Home - TechNet Blogs. It's about the same thing as a "Windows Anytime Upgrade" that you see available in Windows 7 or 8, so no reinstall is necessary.
If I recall correctly this wasn't possible in earlier versions of Windows Server, and that's probably what Reagan is remembering.
Let us know how it goes!
Best regards,
Matt