It wouldn't surprise me if SD was happy to collect a couple hundred a year for giving you a piece of paper that may or may not have validity. They really have nothing to lose.
But it sure sounds like you are a resident/domiciled/(pick your favorite legal term) in AZ.
- AZ likely won't be happy if they find out they didn't get their pound of flesh.
- Make sure your insurance company is fully aware and in writing of the situation. Don't be surprised if they have an issue. If you keep it from them and they find out after an accident, don't be surprised when they don't want to pay out due to fraud.
This is assuming the RV spends much of it's time in AZ and is generally stored in AZ when not in use.
If the RV never enters AZ, you might be legit but still best to check with your insurance and the AZ DMV.