In my experience with Resharper, you'll get this suggestion if you are setting a variable value in the declaration, but the variable's value never changes throughout the method. In that case, it can be made into a local constant. You'll also get the warning on an instance variable that you initialize in place, but never change the value anywhere in the class body.
And the author of that book basically makes the argument that by using readonly instead of const, you can avoid having to rebuild dependent assemblies if you change the value of the readonly value. In contrast, for a change to a const, you'd have to recompile the dependent assemblies against the new version of the assembly with the const.
It's a legitimate argument, however, if a value is not going to change throughout the life of the application, I still think it's better to use const. I like to use readonly for values I'm loading from a configuration, for example, that won't change after being initialized in the constructor.
I think it's much better to have the code clarity that const provides at the possible expense of a little more compilation maintenance.