ode23t and symplectic Stormer-Verlet integration

I have red in an answer related to simulation of particle motion in magnetic fields that the only ode solver ensuring energy conservation is ode23t and it is related on Stormer-Verlet intergration. (<http://www.mathworks.com/matlabcentral/answers/9120-simulation-of-charged-particle-in-matlab>)

I check in help and paper cited in documentation (from Shampine) but I have found nothing which explains how ode23t and symplectic intergration are related, Could you give me some cloue? What I have found about ode23t is that it suits for moderatly stiff problem without numerical damping and it is based on trapezoidal rule