It seems the Homeowners association is gravely concerned with liability. It's a private lake, and one of the conditions for using your boat on the lake is to name the Association as additional insured.
From what I can tell, it's a concern over property damage caused by large wakes.
Their policy for towed devices is here
Item 6 addresses the safety concern over surfboards:
The intended application of Traditional Water Skis, Training Skis, Air Chairs and
Wake Boards/Wake Skates is to be towed behind a powerboat. The intended
application for a Surf Board is coastal wave riding. It was not designed too be
towed behind a powerboat. For a Surf Board to be used successfully behind a
powerboat, the weight of the boat must be disproportioned to its design, thus
creating a large wake. Since Lake Arrowhead is a closed lake environment, this
application presents safety concerns for the Surf Board rider and other boating