Until, finally, various different empirically determined “corrective factors” were unified into the simple equations of General Relativity.

And the people in that alternate Earth could say, “Even though the final equation was simple, there was no way you could possibly know to arrive at that answer from just the perihelion precession of Mercury.  It takes many, many additional experiments.  You must have measured time running slower in a stronger gravitational field; you must have measured light bending around stars.  Only then could you imagine our unified theory of gravitation.  No, not even a perfect intelligence could know it in advance for there would be many ad-hoc theories consistent with the perihelion precession alone.”

In our world, Einstein didn’t even use the perihelion precession of Mercury, except for verification of his answer.  Einstein sat down in his armchair and thought about how he would have designed the universe, and how he thought a universe should look—for example, that you shouldn’t ought to be able to distinguish yourself accelerating in one direction, from the rest of the universe accelerating in the other direction.

And Einstein executed the whole long (multi-year) chain of armchair reasoning, without making any mistakes that would have required further experimental evidence to pull him back on track.

Rather than observe the planets, and infer what laws might cover their gravitation, Einstein was observing the other laws of physics, and inferring what new law might follow the same pattern.  Einstein wasn’t finding an equation that covered the motion of gravitational bodies.  Einstein was finding a character-of-physical-law that covered previously observed equations, and that he could crank to predict the next equation that would be observed.

It is true that nobody knows where the laws of physics come from, but Einstein’s success with General Relativity shows that their common character is strong enough to predict the correct form of one law from having observed other laws, without necessarily needing to observe the precise effects of the law.

So, from a perspective of scientific method, what Einstein did is still induction from evide