There is no doubt that 2 Wranglers exactly alike, same miles and condition, sitting side by side, one has a clean carfax and the other has you carfax. I would buy the clean carfax one if they were the same price. So of course dealers have to take this in account when pricing their vehicles. Check autotrader and other search's for similar Wranglers. See if you can find a like Wrangler with a clean carfax for the same price, and take this to the dealer with you.
With what you describe, if it is all true, I would not have a problem buying this Wrangler as far as confidence in the vehicle.