I'm not sure I understand your question (or what that has to do with it eliminating the negative effects of vote splitting, which to me is a completely different issue than how you resolve one particular scenario).
Proof by counter example is a perfectly rigorous method for mathematical proof. I pointed out a scenario where negative voting could not encode enough expression to resolve both vote splitting instances on the ballot. You reply by stating that Approval Voting (which I did not mention) will not encode all the information needed to resolve an issue unrelated to vote splitting.
I'm highly skeptical that various studies (that by necessity seek to answer very generalized questions) prove anything one way or the other, but I don't really care to debate that at this point.
I agree that it is hard to get a definitive answer. In the absense of a knowing I would stay away from restricting the expression of voters. This comes with a trade off in complexity where the spectrum is something like