This makes no sense. I think you're confusing the amount of charge on either side of the membrane with the concept of electrochemical potential, which is what dictates the membrane potential. If you add more positive sodium ions to the extracellular space, that means there is a larger driving force of positive ions wanting to cross into the membrane, making the membrane potential more positive (just like what happens when sodium ions enter the cell during an action potential). The reverse then of course will be true if you reduce the concentration of extracellular sodium ions: you'll have less driving force, and thus a more negative resting membrane potential, since potassium's contribution to RMP will further outweight that of sodium leak channels.
A little more explanation:
The transmembrane potential of sodium is ~+65mV, hence why when sodium channels are opened during an action potential, there is a massive influx of sodium, making the cell more positive relative to the extracellular space.
The cell membrane also permits some degree of Na+ to leak through during rest, which also makes the resting potential more positive than it would be otherwise, as potassium, which has a high membrane permeability due to a relatively large number of potassium leak channels, has a potential of ~-85mV is somewhat counteracted by a small influx of sodium, causing the resting potential (~-65-70mV) to be less negative than it would be if the membrane were permeable to potassium alone. Thus, if sodium were reduced extracellularly, there would be less influx of sodium during rest, and a more negative RMP would result.
As far as the clinical importance of hyponatremia goes, I'm pretty sure the osmotic effects on neurons are much more significant than the change in resting potential. I don't think a modest change in sodium concentration would change the resting potential all that much, but feel free to plug it into the Nernst equation to check for yourself.