I have a real hard time believing that Chrysler has detuned the 5.7L from 500hp to 370hp. Do they also say they can tune an SRT8 to 600hp?

Tunes can indeed net you a few ponies, but nowhere near what they are claiming.

I'm not aware of any mopar chips out there. No clue what they'd be putting on. And you better bet that if there is it's going to be a "performance part" (Part# that starts with a "P") and thus has no warranty in of itself. Installing a mopar part like that would then void the drivetrain warranty.

Your dealer is not telling you the truth.