The idea that CSA vets were the ones to determine that the stones would be pointed MUST be false. The stones were provided by the FEDERAL government, who would not even consider asking the veterans what they wanted (at least not during that time period).
I personally think it was just a way to make the distsinction between Union versus Confederate stones immediately apparent.
One old reference I came across back in the 1980s (didn't save the reference, but noted what it said) stated that it was UNION veterans who wanted the CSA stones pointed so that of a Union vet accidentally sat on one of the stones he would immediately "get the point" that he had made a mistake. Although probably as mythical as the CSA version, this one would make more sense, since Union vets had more influence with the issuance/style of veterans' stones.