That's a bizarre way of putting it. If Kurtzman was "joined" to anyone at the time, it was Roberto Orci, who had been his writing partner since their earliest days on Sam Raimi's Hercules: The Legendary Journeys a dozen years before and would continue to be until 2014. After their years with Raimi and before Star Trek, they had worked for Abrams on three other projects, Alias from 2001-03, Mission: Impossible III in 2006, and Fringe in 2008-9. They had written movies for several other filmmakers in the interim, including Michael Bay twice. Hardly "joined at the hip." Abrams was one of various people who employed the duo. On ST '09, they were probably the most junior members of a writer's room that also included Abrams, Bryan Burk, and Damon Lindelof. But they went their own way later on, and then split up and pursued separate careers.
I was being tongue-in-cheek.
Clearly, JJ has rubbed off to a degree on Alex Kurtzman.