Firstly, I'm liking your tinfoil hat very stylish, but I have to say jmods don't run around the game on 'normal' accounts looking for bots, a large part of the community don't like bots despite the fact we keep the econ running, and as such try and break visible bots.
Secondly, Jagex has no responsibility to give valid evidence, in TOS your acc can be banned at any point without reason, you don't own your account Jagex does.
Thirdly Jagex moderator comment, means the jmod who applied the ban left a comment on the ban reason, so if you try appeal it, whoever is dealing with it has extra information without them giving away how they detected your rule breaking(more importantly the specific thing they detected) and giving information away as to how they do it, its a internal comment regarding your ban, not that you was banned because a jmod decided he didn't like you and couldn't find evidence that you broke a rule.