Boundary conditions just mean plucking out a specific situation from very general math, like the +c in the solution to a quadratic equation, or initial conditions for a Lagrangian/Hamiltonian that could cover very general general circumstances without limiting to specifics. The potential at infinity just relates to definitions, needed in order to make fair comparisons with fields (it establishes zero or background, but actually can involve non-zero fields).
Frame Invariance shows us that Leibniz was right. It doesn't matter what boundary conditions apply within the system. But of course, the world outside the system is a boundary condition: if you ask 'How will this system impact the world?' you make the world part of the system.
But, there is no absolute frame of reference. Entropy, energy, linear and rotational momentum, are fundamentally relative. So within a system they cannot be evaluated except relative to the system. But when you say how will it impact something outside the system, you change the terms, you shift the question. So in your terms: Earth is a boundary condition, the damage train A or B can do to it arriving from space will depend on relative velocities of A & B to Earth, not just each other. We treat the universe as not rotating, but it wouldn't be detectable within it, if it was - rotational momentum is implicitly defined, as relative to the universe.
A really interesting case of this classical phenomena in tension with the quantum world, is the Unruh Effect. Clearly there are still matters to settle in both theory and experiment.