After sending an e-mail to a Microsoft Store rep, he had the following response:
I apologize for the confusion on this matter. It would have been more accurate, perhaps, to list the system requirements for the Visual Studio 2010 upgrade as "Any Microsoft developer tool," as tools from other software companies do not qualify.
It looks like they may have changed their policies from upgrade versions in the past. Looking at an upgrade box of Visual Studio 2005, I see the following:
The enclosed program will search your system to confirm your eligibility for this upgrade. The software will install only if you are a licensed user of one of the following products:
Microsoft Products: Microsoft Visual Tools, Version 5.0 or later
Competitive products: IBM VisualAge, IBM WebSphere Studio, BEA WebLogic Workshop, Oracle Developer Suite, Oracle JDeveloper, Borland C++Builder, Borland Enterprise Studio, Borland JBuilder, Borland Delphi, Borland Kylix, WebGain Studio, WebGain VisualCafe, TogetherSoft Together ControlCenter, Sun ONE Studio, Macromedia Studio, Macromedia Dreamweaver, Macromedia Flash, IntelliJ IDEA, Intel C++, Metrowerks CodeWarrior, Symantec Visual Café, Sun Java Studio, Borland C#Builder, Sybase PowerBuilder
So obviously they allowed upgrades from competitive products in the past.
Calling a Microsoft rep in the Volume Licensing department confirmed that specifically, they allow an upgrade from any paid previous version of Visual Studio (she specifically pointed out that Visual Studio Express editions do not qualify). She also confirmed that they no longer offer upgrades from competitor developer products (and thus, Eclipse does not qualify).
Now, I don't believe the installer will actually check for anything. I do still have a copy of Visual Studio 6 (in all it's huge-box glory) sitting in my closet, which qualifies me for an upgrade. There's no way to install it on Windows 7, since you require VS2005 for Vista or newer from what I've read. If anything, it gives me a legal standing on the issue.