Has anyone ever heard of a 64-bit OS identifying itself as a 32-bit OS?

We have a Windows Server 2008 R2 x64 development server. We've been trying to activate it with a product key from MSDN, but it keeps telling us the the key is invalid. I've opened a ticket with MSDN for this.

Then something odd happened --

I tried to install a 64-bit version of SQL Server 2005. After it extracted, we got this message:

This version of hotfix.exe is not compatible with the version of Windows you're running. Check your computer's system information to see whether you need an x86 (32-bit) or x64 (64-bit) version of the program...

Now, we're pretty sure this is a 64-bit OS. Computer > Properties says:

System Type: 64-bit Operating System

Also, we have both a "Program Files" and a "Program Files (x64)" directory.

I don't know how the product key activator or the SQL install program attempts to divine the type of OS, but could it be...wrong?