November 18, 2015 03:30 PM

Nearly six weeks since Lamar Odom‘s hospitalization following a near-fatal overdose, the Kardashian-Jenner family is still sticking by the former athlete.

“We’ll always be there to support Lamar,” Kim Kardashian West tells PEOPLE exclusively in this week’s magazine. “You stick by your family and you are there to be the best support system in the world.”

Odom, 36, is still legally married to Khloé Kardashian, 31, though for now they are not getting back together as a couple.

Lamar Odom
Imeh Akpanudosen/Getty

As for the report that Keeping up with the Kardashians cameras were rolling when Khloé, Kim and Kris Jenner rushed to Odom’s side after he was found unconscious in Las Vegas? “So ridiculous,” says Kardashian West. “One big misconception about our family is that we do everything in front of the camera. We really do have such private moments.”

After all, “Lamar will always be family,” says Kardashian West, 35. “No matter how you look at it.”

Keeping up with the Kardashians airs Sundays (9 p.m. ET) on E!

For much more from Kim Kardashian West, including details on her pregnancy and her family’s turbulent year, pick up the new issue of PEOPLE, on stands Friday

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