I would think another MOPAR dealer would sell the right stuff to you.
If not, have your mechanic look at this link. He needs to make sure he is ordering the right stuff for your vehicle. I
If you need only Dexron III, then that is available at all parts stores. If you want to upgrade, Dexron VI is available and backwards compatible. It is a synthetic fluid, much "improved" (both price and performance-wise) than Dexron III.
Re-confirm that the requirement is for Dexron III. No need to buy that at a dealer, and readily available at all auto parts stores.
Many name brands are selling Dexron III as a Dexron/Mercon universal ATF, because GM, the licensor for Dexron, no longer licenses the production of any of the Dexron III fluids on the market, so on a very technical basis, the fluid is not available anywhere else. That said, the UTF meeting Dexron III specs is what I used (and is spec'd for my ATs).
I am also disappointed your independent mechanic is not aware of the Dexron requirement and where to obtain fluids meeting the correct spec.