Russell is in a show (like the old Brother Bear show) for wilderness explorers, and you can meet him after. I don't know where Doug was going, but we ran into him as he came out from backstage on a trail behind the little amphitheater.
I met Dug maybe 10 minutes after the show with Russell. There was a photopass photographer with Russell (in case you want autographs: he does not sign) and he told me to hang around and wait, he was coming back with Dug right away when Russell's meet and greet was over. True to his word he did.
It does seem you have to go to the show to meet Russell. They closed the area off and let no one else in when I watched. I was a solo adult and no one did bat an eyelid. They even gave me the sticker the kids get.