The specific question comes from paintball, which is the reason for the smaller 13 cubic inch tank, but I figured that the math behind it relates equally well to scuba
I think I discovered the source of my confusion. The manufacturer of the 97 cf tank says "97 cubic ft (or 550 cubic inches)": (Air Tanks For Sale Discounts for PCP (Pre-Compressed-Pneumatic) Air Gun by AirTanksForSale )
Holy cow, no wonder there is confusion -- that website is a godawful nightmare