As a previous employee of Chrysler's Warranty Escalation Dept and also Chrysler Service Contracts, we got so many calls from rightly pissed off, confused customers that had no idea what they were sold and often found out what they were promissed was not true due to the dealers information that was provided to "close the deal".
The powertrain warranty only covers internal mechanical parts (gears and stuff) of the main powertrain components, and does not cover any external or attached components unless deemed to have failed due to the fault of a warranted part (dealer descretion).
Also, not to sound picky but to clarify..."extended warranty" is not the correct term and if the F&I guy at the dealer is calling it that; then he doesn't know what he is selling (not surprising). Chrysler does not sell "extended warranties", the "warranty" is set and can not be changed unless so deemed by the manufacturer rep for specific case by case reasons.
Now, you can buy a "Service Contact" on your vehicle. Chrysler Service Contracts sells all sorts of them ranging from everything like one for just roadside assistance to a Max Care which covers about as bumper to bumper as you can get these days. They range in all different time/years choices (which dealers rarely show you except the most expensive ones) and if your at all interested I would HIGHLY recommend calling Chrysler Service Contracts directly for a list. Also...being that dealers are independent businesses, they can sell ANY brand of service contracts they want and are not required to seel the Chrysler ones. Many dealers sell XYZ brand (because they usually have a higher profit margin) and don't even tell the customer up front, only saying it's an "extended warranty." Customer goes to a different dealer while say on vacation because they think they have a service contract and that dealer says, "Nope sorry, we don't service XYZ brand." I would ALWAYS ask the dealer what brand service contracts they sell. Contrary to what they might tell you at the dealer...you can buy a Chrysler Service Contract (on any brand vehicle even) at ANYTIME after purchase within 12 months/12k miles with no penalty, or anytime after that no matter what the time/miles for a small fee ($150 last I checked).
Lastly...you can buy a service contract from ANY dealer willing to sell you one and even directly from Chrysler Service Contracts. A service contract is a retail item and the dealer will mark them up like anything else; so just like the car, you can hagle the contract price or go buy it somewhere else that is willing to sell for less.
Sorry for the long one.