Aside from what silverfox already mentioned, if the signs say "No Motorized Vehicles" as you said, then STAY OFF OF THEM with your moped. Despite the pedals, a moped -IS- a motorized vehicle. That's what the "Mo" in moped means..."Motor". That's that thing making all that noise down there on the frame! It's a MOTOR! The signs are posted...there is no "gray area" here what so ever for you to feel that your rights have been infringed upon. You were in the wrong.
I'm sorry that you seem to feel this is some kind of game but a moped is a motorized vehicle...period. It's not a toy, it's not some sort of custom bicycle, it is a motorized vehicle. If you are really that ignorant then the park ranger had every right to get "pissy" with you and you're damned lucky he didn't haul you in.
Those bike paths were not put there for your own personal convenience. If you can't respect that as well as the rights of others and since you apparently feel incapable of safely riding your moped on proper roads, perhaps you should just park the thing for the safety of everyone (including yourself).