Is (nearly) all data separable?
TL;DR

Yes, with overfitting all data becomes (non-linearly) separable (as long as the points don't precisely overlap).

Explanation

The problem with your argument is that you are using circles on a 2D plane, which is very difficult to learn. However, I think your argument can be made stronger with a decision-tree.

(0.2, 3.1)? --&gt; yes -&gt; star
            \-&gt; no  -&gt; (1.2, 4.5)? --&gt; yes -&gt; circle
                                   \-&gt; no  -&gt; (x1, x2)? --&gt; yes ...
                                                        \-&gt; no  ...


Decision trees are well accepted models, but note that they are non-linear models. With that, it is easy to argue that all data becomes separable.

However, the issue lies with overfitting. Because models like that become unstable with data points that were unseen before. So, just because the training data is separable, it doesn't mean that the models generated from it become any useful.