It's OK. We understand that new people to the board tend to make these kind of mistakes. This is common when people do not understand where to find this information. You may have been posting for a couple of months but you are not yet accustomed to finding the text of actual "laws".
What you shouldn't get in the habit of doing is making personal attacks on those who are trying to help you. Seeing how I can help you find the actual laws, I am far from worthless to you. The sooner you set aside your eagerness to insult and find a willingness to listen, the sooner you will learn something which will benefit you highly. Unless you are in your 80s, I would refrain from using terms like "sonny".
Like I suggested, go to the actual Statute or DNR Admin Code. The site rules require that you cite to authority. This means giving a Statute or Admin Code, etc number for reference. You make the off-hand insult that my data is not reliable yet I am the one who is citing to authority as is required. You made the rookie mistake of quoting the little paper pamphlet that you get free with your license. Those are glorified FAQs and have zero authority or enforcement power. They contain zero actual laws. They even give you a disclaimer on the cover. This one is from the deer pamphlet but all are similar..
Regarding the actual laws, the DNR only has control over DNR Administrative Code. They do not have any control over Statutes although they have the authority to enforce them. That is why 167.31 is not a "DNR rule".
If you go to the actual Statute you will find that a pellet gun does not meet the definition of a firearm for the purposes of 167.31. This means that there is no "law" requiring a pellet gun to be in a case.
Here is where you find Statutes
https://docs.legis.wisconsin.gov/statutes/prefaces/toc
Here is where you find the DNR Admin Code
http://legis.wisconsin.gov/rsb/code/nr/nr1.html
What you want is NR10 for "hunting" DNR Code..
http://www.legis.state.wi.us/rsb/code/nr/nr010.pdf
If you need help with what Statute pertains to what law you can simply ask. I and others are willing to help you get up to speed.