So are people jealous, envious or both? It's true some tribes have no regulations on hunting but not all tribe are like that. Most tribes are now switching or have switched to regulated hunting on reservations. It is up to the discretion of the tribe how they want to manage the wildlife (all tribes are considered sovereign nations in the eyes of the US Government and are under trust. Hence most wildlife projects on tribal lands are funded by USFWS grants.) The tribe may have had an agreement with the State that once the population was healthy and numbers were at a surplus, then there could be limited harvesting (at least I hope) perhaps something that was not mentioned when the the project had begun (for this particular reason). What if the situation was a bit different and the sheep were placed on public land bordering and the sheep decided to setup camp on the reservation? Its still a publicly funded project but the animals are going to go where they feel comfortable, they don't see the lines we draw on paper. The tribe would still have the option to manage the sheep as they see fit. Maybe they wouldn't want them and so they killed them all or they told the state they had to spend more public dollars to trap and remove all the sheep. Which would be more upsetting? The government (state and federal) is going to spend public money how they see fit. Whether we agree or not. I don't agree with the government using my money to pay politicians or go to war but they use it anyway.
Earlier someone was right about turning it into a possible "cash cow." The Apache tribes of AZ and NM figured this out about 20-30 years ago. But that is no different than a private land owner charging "X" amount of money to hunt a public owned animal on their land. This tribe could have done the same, but perhaps they chose to think of their tribal members first and gave them the opportunity to hunt these animals for a fee which tribal members can afford. Maybe in the future they will have tags for non-members, but of course its anyone's guess at how much they're going to charge. They can then use those funds generated from selling tags to do more wildlife work.
Finally, by telling us to go back to hunting without firearms, modern technology, etc. is sort saying all farmers now have to sow their fields with only a mule, goods have to be sent by wagon train, travel is only to be done on foot or by horse or how about lets defend this country with only muskets or even just swords. It's not going to happen.