I think the interpretation is "take the volume of fresh surface water on Earth", then "make that volume into a perfect sphere", and the diameter of that sphere is smaller than NYC.
I don't think that is even true. This may refer to the total volume of potable water. between the great lakes and Antarctica, there is lots of non-salt water out there. Easy google results show 35 million cubic kilometers, which is a rather large sphere.
The volume of the Great Lakes, per Wolfram Alpha [1], makes a sphere ~22 miles in diameter. The Great Lakes is ~20% of the world's surface fresh water.
Your number of 35 million cubic kilometers includes the Antarctic ice sheet, but the definition of "fresh surface water" sounds to me like it intends to exclude the ice sheets from the list.
