Can Newton's first law truly be tested on earth? Newton's first law determines that a body which does not participate in any interaction with any other body, will retain constant velocity (in an inertial frame of reference). To test the law empirically, one can think of an astronaut throwing a ball off a spaceship, somewhere deep in space. As it moves in the void, the ball does not interact with any other object (except some negligible effects) so we can measure its velocity and confirm Newton's law (assuming that our spaceship serves as a good inertial frame of reference).
To me it seems that leaving earth is logically necessary to test Newton's first law. Every physical body on earth participates in a non-negligible interaction: the earth's gravity, obviously. That's supposed to ruin everything! Of course, the well known earthbound experiment in which a body is pushed over a frictionless surface exhibit similar results. The common explanation for that is that the interaction with the surface perfectly cancels earth's gravity, so it's as if there's no interaction at all. But logically, without already asserting Newton's laws, we cannot claim that the two interactions cancel each other like that. Claiming that this experiment confirms Newton's first law is a circular argument. Will physicists agree with me?
Note that if I'm right, it means that when Newton asserted the first law, strictly speaking it wasn't an empirical fact,  but "merely" a logical generalization of known empirical facts.
 A: 
it means that when Newton asserted the first law, strictly speaking
it wasn't an empirical fact, but "merely" a logical generalization of
known empirical fact

This is true for ALL laws of physics.  ALL of them are logical generalisation  of known empirical facts.
That is how science works. That is how science is supposed to work. We take a set of observations, and we generalise them into a law that all those observations comply with.
No matter how many observations in how many different environments you take, you can never be 100% sure, that the law will also apply in every other environment. The more and more sets of observations that we come across that follow the law, the more confidence we have in the said law.
In case of Newtons' first law, it has been able to explain all the sets of observations that we have come across. Hence, we have a high degree of confidence in it.
A: The main point of Newton's first law of motion is that there is no a priori acceleration. Every acceleration we see can be accounted for by interactions between bodies. This we test everyday - if a stone is falling on the ground, we can compute acceleration from force laws for gravity, air resistance and so on.

To me it seems that leaving earth is logically necessary to test Newton's first law. Every physical body on earth participates in a non-negligible interaction: the earth's gravity, obviously.

This is why, I think, it took over two milenia from Aristotle and Archimedes to Galileo and Newton.
Earth bound experiments will be influenced by non negligible force of gravity, that you cannot shield or manipulate. In Earth it seems, there is indeed a priori acceleration - the downward one! Not only it seems that way, by itself it makes no sense to declare this acceleration having source in the interaction with the Earth, since a priori acceleration is much simpler explanation of everything that was observed and gravitational law would just complicate the theory.
I think historically the change happened when Galileo constructed his telescope and looked at the sky and saw moons orbiting other planets. It looks as if they are attracting each other and there is no a priori downward acceleration. The generalization that the downward acceleration on the Earth also originates from interactions with it is now but a step away and finally sensible to make.
So indeed you are right. Earth bound experiments are insufficient for showing validity of the First Newton law, but observing solar system is.

Note that if I'm right, it means that when Newton asserted the first law, strictly speaking it wasn't an empirical fact, but "merely" a logical generalization of known empirical facts.

Not really, as Newton had empirical facts at his disposal - the mentioned observations of solar system.
A: First of all, no experiment can ever prove a physical theory, because even for the simplest laws not every possibility can be tested. For example, if the astronaut in your example throws a football off his spaceship, how can they be sure that a basketball, or even another football would not behave differently? The simple answer is, they can not. This also means, though, that every experiment will always rely on additional assumptions about what parameters do not influence the result.
Secondly, in the experiment with the body on the frictionless surface, the important aspect is that the system behaves as Newton's laws predict it, which means the experiment does not contradict the theory. Keeping in mind what I wrote in the first paragraph, this is about as good as it gets. Generally, physicists try to describe and predict how a system will evolve. If there is a theory which predicts the evolution of a system well, it is a good theory and in this case, for the prediction of the behaviour of the experiment with the frictionless surface, Newton's laws fulfill this requirement.
To be clear, applying this point of view, there is no circular argument here: We assume Newton's laws and make our prediction, then we conduct an experiment and see that everything turns out as we predicted, so the experiment confirms the theory by not contradicting it.
