Every couple of years, my wife and I backpack in the Wind River mountain range in Wyoming. Maybe it's not the completely primitive experience you had in mind, but we backpack in with pasta, rice, dried beans, dried potatoes, some spices and dried tomatoes, and some hard cheese like parmesan, and don't come back out for a month or more. We fish for our meat, which isn't all that hard once you get a day or more off the trailheads. We generally camp by any of a thousand lakes, and after we set up our tent, she might say, "I'd like to start dinner in about 15 minutes; could you go catch us a couple of fish?" And in 15 minutes or so, I come back to camp with a couple of nice trout.
It isn't uncommon for us to go 3-4 days in between seeing any other people.
I remember the last time we were there, we were cooking on a backpacking stove next to a huge boulder, near a lake. On our other side was a hedgelike bush. What looked like a yearling deer stuck his head around the bush and watched us cook for a minute or so. As we stared at him, he stared back at us, and we could imagine his mental conversation going on: "Uh oh, they don't seem to be afraid of me, so maybe I should be afraid of them!" And he ambled off at a fast walk. One time, a deer bent down his head and looked into our tent in the morning. I don't think he had ever seen such a thing before.