When you refer to the 'speed of the wave' I assume that you are referring to the speed of the wave front towards the shore. Of course this speed affects the speed potential of board and rider, for the simple reason that increasing the speed also increases the rate at which the wave lifts ( all else being equal). This increases the rate at which the board and rider can acquire gravitationalpotential energy, and this allows board and rider to convert the potential energy into kinetic energy at a faster sustainable rate. This leads to greater speed ( again, all else being equal).
The interaction between the surfboard and the water ( hydrodynamic forces) create necessary lift and allows control of the direction and trim angle of the board (and thus also the fall line as well) all of which is required for the acquiring and conversion of gravitational potential energy into kinetic energy. Hydrodynamic forces are also created via muscular input from the rider, these can be used to propel the board also.
Please address your comments to the subject matter, without making spurious and illogical ad hominem and 'from authority' arguments. The argument from authority is particularly hopeless when it misinterprets what the information from the source actually implies.. as you have done.