Whats the yard - stick to decide on topic - off topic?
Is the post related to the OP in any way? If not then it's off topic. I don't generally censor replies just for being off topic, a couple here and there are harmless, only if they break another rule as well (trolling, ad hom, etc).
Is there a recourse to moderators , who falsify decisions to their will?
Yes, admins can see pretty much anything mods can do so it would be pretty hard to falsify anything.
Is there public scrutiny provided about which moderator decided what?
No.
And to reply to an older post
...so if someone does not agree with a comment and reports it as off topic then it will be deleted regardless of how on or of topic it may be. ...
No, reports are just suggestions, I look at each objectively.