Actually, it would be unusual to find Union and Confederate soldiers buried side-by-side on the battlefield or at the field hospitals. I have a partial list of Confederate dead at Camp Letterman and they were buried in at least nine rows containing 30+ graves in each row. Without further analysis I can't rule out Union soldiers being buried among those Confederates but my guess is they were not. Could you provide further details on the New York soldier?
It was my understanding the Union and Confederate wounded were segregated at Camp Letterman, and further, the Union soldiers were evidently grouped by corps. For example, the First Corps was assigned 16 tents holding 192 beds (divided into wards, 48 beds to the ward, each under charge of an Assistant Surgeon), the whole under charge of Surgeon William Fisher Norris.
Would your ancestor happen to be T. K. Lawrence of Company G, 24th Georgia, who died on August 19? He was buried in Row 3, Grave 35. He was reportedly reinterred at Savannah (Laurel Grove) in 1871. A different list had him in Row 1, Grave 39, but that appears to be an error. After the war, the North Carolina burials at Camp Letterman went to Raleigh, while others went to Richmond (Hollywood Cemetery).