A. The Example
The difference is that your statement is not a theory. To be a theory it must make predictions as in an “A implies B” form, and be generalizable.
The University of California, Berkley, defines a theory as
A broad, natural explanation for a wide range of phenomena. Theories are concise, coherent, systematic, predictive, and broadly applicable..
B. Theories in physics in general
The interesting question is whether any physics theory could even be true - hotly debated in philosophy of science as discussed below. Theories usually introduce mechanisms and notions about physical reality on top of their predictions.
Secondly, showing it will never be falsified is not only impossible, but we can’t even claim to have high confidence. We continue to get better at both measuring and at creating extreme conditions, and we have observed other theories fail under new conditions. There are even theories that the laws of physics vary through space and time. One example is bubble universes, and another is inflation.
The meaning of “a true theory”
Assume we somehow can show it will never face a direct counter-example. We’d still need to know what it means for a theory to be true. In logic, “A” is the same as “A is true”. But for physics, some (e.g. below) say predictive capacity is not the same as true representation.
For example, electric fields are used extensively, but we do not know that they exist per se, nor whether the question even has meaning. We know charges exert forces by Coulombs Law. That is indisputable and arguably primary. An infinite variety of charge distributions can result in a certain net force on a unit charge at a point. For tractability, the magnitude of an electric field at that point expresses the same information.
So the question is whether Maxwell’s equations are “true”. If we say that electric fields are real and that theories using them as primitives are “true”, then what about electric potential? That’s the energy in this field that we now say exists. Does that exist? Potential is the energy (as work) it would take to bring a unit-charge to that location. These and other questions are debated in philosophy of science - as is the whole notion of physical theories and truth.
The same type of thinking applies to gravity. From Forces and Fields by Mary B Hesse
There is a physical difference between a gravitational field ... and the velocity field of a fluid. In the latter case the field function is an actual property of material at every point of the field, but in the gravitational case the potential function V is 'potential' in the sense that it does not necessarily describe a material property of the field ... it describes a potential property, namely, the force that would be exerted if a small mass were introduced into the field at that point.
Despite her claim that the case is simpler, debate has sprung up about the reality of the stream function. We would at least need one fluid particle to travel the entire streamline for it to be real. As hydrodynamics has advanced, the shape of the water molecule itself is being taken into account, such as here: https://pubs.acs.org/doi/10.1021/acs.jpcb.6b01012
( The basics of including molecular dynamics into hydrodynamics: https://www.redlandsusd.net/site/handlers/filedownload.ashx?moduleinstanceid=16224&dataid=10931&FileName=Water%20Properties%20Activity.pdf
No particle follows the streamline: I would say that means we have realized streamlines don’t actually exist - depending again on what we mean by existing, even though models using them do work.
Inability to Predict future counterexamples (direct falsifications)
You alluded and another answer alluded to this: Our capacity to measure has been advancing and our capacity to create extreme situations has too. Things like capturing images the infant universe, and the Haldron Collider, are good examples respectively. Perhaps e.g. at new power densities .. the theory no longer works.
Because you ask about proving, the relevant supposition would instead be, “Suppose that all the observations that have happened and will happen agree with the theory and we know this fact now”. Which reformulation implies its own answer.