Oksana Grigorieva's bodyguard/key adviser told her none other than Jack Nicholson was footing the bill for his services because Jack was so concerned for her safety ... but his story is pure BS -- sources tell TMZ.
We know Kristian Otto Herzog -- a twice-convicted felon who impersonated a cop with a loaded firearm -- told Mel Gibson's baby mama he would protect her free of charge, because Jack was graciously covering the bills.
Herzog showed Oksana this photo -- posted on his Facebook page -- to show he's done work for Nicholson in the past. The photo was taken at The Ivy restaurant. But we're told Nicholson doesn't know Herzog from Adam ... and Herzog just inserted himself in the photo as Jack was leaving the restaurant.
Herzog has become Oksana's key adviser who is now calling all the shots. TMZ broke the story ... Judge Scott Gordon issued a restraining order Monday against Herzog, ruling he posed a danger to baby Lucia and prohibited him from going near her.