I am not a positivist. Positivism states that what cannot be observed does not exist. This conception is scientifically indefensible, for it is impossible to make valid affirmations of what people ‘can’ or ‘cannot’ observe. One would have to say that ‘only what we observe exists’which is obviously false.No, Einstein is wrong.
Albert Einstein in an interview with Alfred Stern, Contemporary Jewish Record 8, 245–9 (1945); also in A. Calaprice, ed., p. 253
Positivism does not say "what cannot be observed does not exist." Positivism does not try to describe things that are unobservable or nonexistent. Those are metaphysical issues that positivism was invented to avoid.
Einstein's biggest influence was to turn theoretical physicists from positivists to anti-positivists. The anti-positivists are always making pronouncements about things that cannot be observed or tested. It is the modern equivalent of arguing about "How many angels can dance on the head of a pin?".
Science is all about explaining what can be observed or tested. Once you start debating the existence of things that can never be observed anyway, you have left science. Such questions are meaningless, in the sense that no one can prove you right or wrong.
The positivist conception is the core of science, so of course it is scientifically defensible. Einstein's view is not. We can make all sorts of valid affirmations about what we can or cannot observe. Most of science is about what we can observe. There are also lots of examples of what we cannot observe, with famous examples being Heisenberg uncertainty (cannot simultaneously observe position and momentum of an electron precisely), and black holes (cannot observe any dynamics inside the event horizon). A simpler example is that you can burn a letter to make it unreadable.
Special relativity is the main reason Einstein is considered a great genius, and the main reason he gets credit is that he denied the existence of the aether. He did not really deny the aether any more than Lorentz did, but people think he did.
Poincare had the more correct posture. He said that the aether was unobservable, but it is convenient for some purposes.
So Einstein is more famous because he said that the aether does not exist, but he later denied that it is possible to ever say that something is or is not observable!
I would have thought that Einstein's bad philosophy would be abandoned by now, but the opposite is true. More and more, physicists insist on making big claims about parallel universes, strings, and other unobservables.