What's the proton concentration around a DNA helix?
DNA stands for deoxyribonucleic acid. Acid, by definition and mechanism in aqueous environment, is something that donates proton ($H^+$). HCl dissolved in water will donate proton to solution, thus bringing pH down, since $pH=-log_{10}[H^+]$.

DNA, being an acid, donates protons to water and brings pH down a notch. Just like in case with HCl, it has nothing to do with keeping charge neutrality. Water is not a buffer, that is able to tolerate or smooth change in pH. What happens when you add DNA to buffered solution, say phosphate buffer, is completely different story from biochemistry.