Yes, it does absolutely address wildlife being held in trust for the citizens of the State and that wildlife "ownership" has no correlation to where said wildlife resides (private, State, or Federal land). Many good reasons for that and the courts have upheld that via many lawsuits and litigation mentioned in the link I provided.
Its already been pointed out that many states allow NR's no access to their wildlife, Wyoming could do the same thing.
Further you may want to look into S. 339, the reaffirming of a States rights to not only Regulate the wildlife within its borders, but also the right to discriminate against NR via price or even to allow ANY NR access to its wildlife.
https://www.govinfo.gov/content/pkg/BILLS-109s339rs/pdf/BILLS-109s339rs.pdf
Passed in 2005, in response to the Taulman lawsuit against Arizona where Taulman(USO) claimed NR's were being discriminated against based on the Dormant Commerce Clause in Article I.
No, I really don't care one way or the other if you apply for tags in Wyoming, or Alaska, or Oklahoma, or any other state. Doesn't impact my decision to do so, other than perhaps making my odds of acquiring tags as a NR easier. If you don't like the facts of State Rights or how any State chooses to regulate their wildlife, don't apply, simple as that.
I apply in 10-12 States many of which I've been doing so for 20-38 years, and in the case of some, have never drawn a single tag (NV, UT, and ID).
I view my application fees and required hunting licenses as a contribution to help those States take care of, manage, and protect wildlife. That way if I do happen to draw, I'll have some quality hunting opportunities. If I don't ever draw, that's OK too...I care about wildlife and I'm willing to apply and buy licenses, even if my contribution doesn't directly benefit me via a tag.
In the case of some States, I've been the beneficiary of receiving a license that many have applied for a lot longer than I have, and contributed way more than I have (Arizona Desert Sheep, Musk ox in AK), to name a few. I appreciate that those States even allowed me to apply, let alone hunt those animals when many Residents will never get the opportunity.
Frankly, as a NR I not only believe I should pay more, its within the law for any State that I don't reside in to discriminate against me when it comes to NR licenses to hunt and fish.
I'm also very grateful for any State that allows me any kind of access to their wildlife, as has been noted, they aren't required to.
If you think you have a case that land ownership should grant you equal access to a State's wildlife, as Randy said, file a lawsuit and knock yourself out...