A Nature blog post critical of the study. Their objections are different to mine but I agree with them too.
I agree with most of them, too. There is no way around the fact that the lac promoter is leaky, so you will always get some expression. This will bias your results, even in the absence of induction with IPTG. Even after a few generations, their library will be skewed away from lethal and neutral mutations and towards slightly beneficial and beneficial mutations. That selection will be skewed once again when you have strong over-expression with IPTG.
One could also easily argue that a specific gene is slightly beneficial with low expression, but deleterious with high expression. This may be why they see stable variation with no induction, but changes after induction.
Either way, they seem to have found beneficial genes among random sequences. The real question is how common are they?