LOL– anything is teethworthy from the Basenji perspective! Just like you buy them a basket full of toys and their favorite is the empty spaghetti box "found" in the trash.
It seems to me there are a couple of issues here. I don't think a shelter wants just any JoeBloe walking in one day to say "hey I'd like to help by walking your dogs". The shelter needs to know something about its volunteers though a criminal check might be a bit much. If someone has been volunteering at a shelter for some time so the staff knows them and now new policies are being put into effect, then the shelter should have some sort of informational meeting/handout for all its volunteers so they know what and why. And even when volunteers have been accepted, some mini-training should be included for handling dogs. Many shelter dogs have been abused so I wouldn't want a volunteer who grew up under the "old" system of training with spanking and collar yerking now handling a special needs dog. Actual certification for dog walkers - no - the government intrudes enough.
I've made a lot of trips around Sacramento. There are a lot of nice areas there. The climate is a lot more temperate than CT. Good luck in The Golden State!