Not necessarily. If their algorithm demonstrably implements the necessary calculations, and their implementation demonstrably implements the algorithm, then their solution is demonstrably complete.
Is there possibility for error in the execution? Sure. But that doesn't actually necessarily undermine the solution either.
Just as you cannot prove that this posting accurately represents what I have posted in it, you cannot prove that their solution is inerrant. But just as you can demonstrate that this posting does accurately represent what I typed, their solution can be demonstrated to be correct.
Perhaps it would help if I explained a bit: we say that 1+2=3 not because it is provably true, but rather because it is convenient for us to say so. Mathematics is a branch of Philosophy, not of Science.
