Not OP, but I follow a similar process when I have to do coding interviews. I work around the "no public code" problem easily: "great, then pick an open source library you use regularly and let's go through and look at some of the things you do with it, what you like about the API design, and some things you stumble over or wish were better".
I've had candidates go through everything from jQuery to D3 to Spring to just parts of the Java SDK.
Also, in my experience, the percentage of people who have _zero_ public code is small. Maybe 10%. Certainly not half.