The SpecificVersion property is just a build directive for the Visual Studio compiler. It causes the latest version of an assembly that can be found to be loaded when you compile. It doesn't have any effect on your assemblies at runtime. Your assemblies will require the version of a dependency that was used to compile them. The exception to this is the presence of a policy assembly for the dependency to point your assembly to a newer version of the dependency. ESRI did not supply policy assemblies at version 10. I don't know if this is going to be the case for 10.1 but unless they do you will need to recompile against the newer version.