RJ did not kill the private investigator.  If it had been RJ, RJ's signature background music would've been playing in the background during the drive to her house, the fight, and after her death.  The tiger tiger group killed her because they were the ones that needed to spy on Jane to see how much he knew.  Jane has always known when a killing is RJ so Jane calling her death a RJ killing is a red flag.  Also, the tattoo being three dots seems a little sketchy.  She could've just been trying to point to her shoulder and failing to hit the same spot because she was dying.  If it was RJ, then where was his taser?

Jane knew it wasn't RJ but he's about to use it as an excuse to get the rest of the suspects together.  Why would he do that knowing the tattoo wasn't RJ's?  Because the suspects are fake.  A fake list of people that have acted suspiciously toward Jane to fool RJ into thinking he's safe because Jane somehow missed him.  Let's be realistic, RJ would kill Jane and the whole team if he found his name on Jane's list of names.  RJ might enjoy games, but he never risks actually getting caught.  And Jane would never endanger Lisbon/team by telling them the real suspects' names.  

I'm guessing that in the next episode Jane will gather the fake suspects to his house, he'll search for the tattoo and the tiger tiger suspects will all have it.  Jane will let Stiles and maybe Haffner go because they're Visualize and don't have a tiger tiger tattoo.  Jane will then fake his death along with the tiger tiger suspects by blowing up his house using a stolen drone from episode two.  Lisbon will be completely unaware that Jane isn't dead and her grief will convince RJ that Jane really is dead.  This all fits with what is seen in the 6x06 preview: http://www.youtube.com/watch?v=JhqIiOERZeY 

The 6x07 episode press release reads: "Following the shocking events at Jane’s house, the Red John list is narrowed down further, and the CBI’s priority is the remaining suspects"

Lisbon will think that Jane missed RJ and that RJ blew up Jane.  She will then put all her focus into Stiles/Haffner because they must be RJ since they were the only suspects that weren't in the house when it blew up.  Notice that the press release says CBI not Jane, because Jane isn't involved at all because he's presumably dead.  Meanwhile Jane is free to really look for RJ because RJ thinks he's dead.  Jane's real list is probably narrowed down to two or three people.  Maybe he'll pay each of them visits or break into their houses.  I think he cross two of them off his list in the seventh episode and be force to call Lisbon for help because one of the break ins doesn't go to plan and he can't risk RJ finding out he's still alive.  By the end of the episode, Jane will know who RJ is but the audience won't.

Now Mashburn is my favorite suspect for various reasons including his mild dirt phobia but rate this theory based on Jane blowing up his house and faking his death and RJ being someone that is not on the list of seven suspects.