I would still place the difference the other way. I'd give naive Kasparov (even) better odds against naive you than I would give trained Kasparov against a you of equal training and experience.

Well the chess is prone to ties, so maybe I'd be able to reliably tie the Kasparov if we had equal training and if I am nearly as smart as him. I do think though that my chances at winning would be massively better if we both played chess for first time after reading the rules off a book. I think it'd be close enough to 50/50 at start with him gaining the lead with each next game, winning reliably after some dozen games.

But the point with the legal debate is that one side is right, and other side is wrong; things do not start off symmetrical. Say, we are to put random people to play chess, with one side missing a queen. I play chess; it seems totally self evident to me that among trained players the one lacking the queen will be guaranteed to lose, while for the untrained players the outcome will be much more random.

For the trials I think the original point was to educate the jury, paralleling the teaching of rules to the chess arbiter. The jury doesn't need to think very hard to verify an argument, it only needs to know the valid rules of reasoning. Suppose we were to have a debate on some fact of mathematics, one real well trained guy trying to prove Pythagorean theorem and other real well trained guy trying to prove something wrong (e.g. approximating the hypotenuse with staircase and proving c=a+b). In front of the jury which decides. With today's jury, chances are the jury would be unreliable in their decision. But it is a fact that trained mathematicians are not so easily misled.