The statement "More wisdom potentially gets extracted when you apply Statistics to more (and better) data, but the analysis itself doesn’t improve with better data." simply isn't true. A hierarchical model, for example, is increasingly able to model subgroups and additional levels of hierarchy as more data are added. Penalized regression (or Bayesian regression) is another example -- the model is structurally different as you change the quantity of data.
The difference between ML and statistics is entirely semantic. Is logistic regression a ML method or a statistical method? It is both!
The difference between ML and statistics is entirely semantic. Is logistic regression a ML method or a statistical method? It is both!