I figured it out. You can add diagnostics to the *.fakes settings file. This enables debugging output when generating the fakes assembly.
<Fakes xmlns="http://schemas.microsoft.com/fakes/2011/" Diagnostic="true">
When I did this, I got this output:
unstubbable: method is abstract and could not be stubbed, type System.Globalization.CultureInfo is not available in the target framework version
SharePoint 2010 targets .Net version 3.5. My unit test was set to target framework .Net 4.0. I changed the target of my unit test project to 3.5, regenerated the fake assembly and voila! It worked!