Now here is an interesting National Cemetery fact. Almost all of the National Cemeteries are under the control of the VA. (Click here: http://www.cem.va.gov/nchp.htm#MS ). But neither Arlington (under Army control) nor Vicksburg are on that list. Vicksburg appears to be under NPS control. Now, if you count the entire park instead of just the cemetery, you might be able to get the most acreage.
Here's another claim about Vicksburg: " Vicksburg National Cemetery has the distinction of having the largest number of Civil War interments of any national cemetery in the United States." http://www.nps.gov/vick/natcem/nat_cem.htm
Andersonville is also a NPS facility, as is Shiloh. So I wonder if the Vicksburg statement would be true of NPS National Cemeteries, or non - VA national cemeteries.
Again, your research is impeccable. I'm guessing that by the time the government statisticians said "2nd largest under NPS management", and it reached the webmaster it got watered down to "2nd largest".