TMZ broke the story .... Kristian Herzog -- who has served time in jail for impersonating a cop -- claimed to have been in an intimate relationship with Oksana that began in May. Oksana's lawyer, Dan Horowitz, told TMZ last month -- with Oksana looking on -- Herzog's claim was "ridiculous".But TMZ has obtained an email Herzog sent to Martin Garbus, another one of Oksana's lawyers, on November 6.