All I have to rely on is the National Electric Code, I refer you to Section 250.53 (G), "The electrode shall be installed such that at least eight feet is in direct contact with the soil".
It also states that if bedrock does not allow a rod to be driven 8 feet, it can be buried in a trench 30 " deep. Can't leave any exposed then.
This all can be found at:
NFPA 70: National Electrical Code®
This is a bit cumbersome to get to the actual reading, I have the instructions to get to this code in the Read This First post of this forum. I hope it is clear enough for you to get to the actual code I cited.
Always keep in mind that local codes may supersede the national code. The NY site is for Home Inspectors, they may or may not know local code, they are not the Authority having Jurisdiction of New York, only home inspectors.
Rods not driven in completely loose effectiveness. Also, 250.70 states that the ground rod clamp that will connect the wire to the rod needs to be rated for direct burial.