Feel free to read the actual case law that contradicts you.

This appears to be incorrect. CPL § 140.10 requires that a petty offense be witnessed by the officer for an arrest to be made, but it doesn't say the same about the issuance of a ticket. And People v Boback (23 N.Y.2d 189 (N.Y. 1968)), a NY Appellate Division court held that a traffic ticket could be issued based on information and belief.

They regularly falsify 311 call records. They say they responded and the offender was gone or that no action was necessary when the condition is still observable.