I am not an electrician but I listen to electricians and have been told several times by different sources that the NEC requires all ground rods in a system to be all connected together with copper wire that is one piece or uses approved connectors, or is thermowelded or somehow otherwise connected in an irreversible manner. The reason as was explained to me is that if there are two grounds, not directly connected together, there can be a difference in potential between them. That can cause malfunction of devices in the system. I do not remember all the details, but do know I have been instructed to avoid ground rods that have no direct connection between them as previously described. FWIW, When I built our cabin and did the electrical myself the inspector checked to see how my ground rods were connected and passed the installation.
When you connect to a campground electrical distribution system you become part of that system. Therefore you should not place a ground rod that is not directly connected to whatever other ground rods there are in the system.