(1) The right to a jury trial does not attach to a traffic ticket in any jurisdiction of which I am aware.
(2) Cross examination is done by parties, and is not the the job of the hearings officer, the judge, or the court.
I truly wish you the best.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
Crazy, isn't it, that you don't get to confront your accusers. Unfortunately, it is the law.
How would the officer confuse your car with your roommate? The car that was parked the wrong way got the ticket. Since it does not affect your insurance, then that is why there is no right to a jury trial. (You have a right to a jury trial on traffic matters at least in Texas. The other lawyer is incorrect on this point. This is because there are collateral consequences - points on your record and raised insurance rates.)
The law no longer permits you to have a jury trial for a parking ticket. Be careful because the state is trying to do the same for speeding tickets as well. The state's current foothold is the red light camera.