No, falsification didn't prove Einsteins theory. It simply failed to disprove it.
Let me put it another way. Say that I have a theory that all swans are white. This is a testable (falsifiable) theory. I then survey all the swans in North America and all are white, the prediction was correct. Ditto for Europe and Africa. Have I proven the theory? No Can I prove the theory? No
It so happens that there are black swans in Australia, but that doesn't really matter, all that knowledge can do is falsify the theory. The best I can hope for with the theory is that it doesn't get falsified.
“Let me put it another way. Say that I have a theory that all swans are white. This is a testable (falsifiable) theory.”
Please do not insult me with this academic sophistry. That is exactly what an unscientific (unfalsifiable) hypothesis is. It’s what has become wrong with all science. Real science is cannot be done by surveys, just because it is never possible to know you’ve surveyed everything. It is exactly this kind of nonsens Popper was trying to prevent.
Here I have a theory. Weakened infectious organisms can be injected into a person and it will make them immune to the disease the organism causes. Of course it can never be proved, right?
I have another theory. It is possible for humans to fly in machines that are heavier than air. Can’t be proved though, right?
I have another. One day men will be able to fly to the moon and back. Of course science cannot prove that?
Another unprovable theory I have is that people can be made to feel no pain while being operated on.
You stick with your post-modernist academic rejection of all knowledge and I’ll stick with reality.
Hank