Is there such a thing like the machine learning paradox? O'Reilly recently published an article about the machine learning paradox. (link)

What it says goes basically like this: no machine learning algorithm can be perfect. If it was, it means it is overfitting and so it is not really perfect because it will not perform ok in real world scenarios.

I searched and I couldn't find any other references to this paradox. The closest I got is the Accuracy Paradox, which says that the usefulness of a model is not really well reflected in its accuracy.

This doesn't sound quite ok to me. For example, a linear model could be perfectly learned, "overfitted" and predicted in the real world. So I suspect it is really about finding the right set of data points from which the results can be inferred. This is, we are trying to approximate from uncertain data, but with the right data we can stop approximating and start calculating.

Is my line of thinking correct? Or is there really no perfect machine learning?

UPDATE: In the light of currently received answers, I think my last paragraph (my line of thinking) can be rephrased as: If we have a model simple enough, why can't we overfit the model, knowing that it will behave correctly in non-trained data? This assumes the training data completely represents the real-world data, which would imply a single model that we can train on.

Keep in mind that what we conceive as "simple" or "feasible" is arbitrary and only depends on computation power and available data -- aspects with are external to ML models themselves.
Basically Machine Learning is used to solve problems for which giving exact solutions is not (practically or theoretically) possible or feasible. If you have a problem that can be solved with exact and proven methods, you don't need Machine Learning. So Machine Learning is rather about finding solutions by approximations with some error margins. In this sense such systems will never perform perfectly and there always will be room for improvements.
(Many real world problems can not be solved perfectly because they are not simply complicated, but chaotic.)