The reason Putin is tied to “organized crime” is because, historically, the KGB controls organized crime in Russia. Russian mobsters are almost always KGB/FSB agents. Sex-slavery, kidnapping, drugs, all of these things serve more than one purpose: money, but also political subversion.
There is organized crime, and then there is organized crime.
I remember reading an article more than 10 years ago that KGB aggressively infiltrated organized crime in Soviet Union while Yuri Andropov headed the agency, ostensibly to fight crime. Eventually, KGB took control of all organized crimes.