Its a typical dealer BS move... The manufacturer offers a warranty, the dealers try to convert you to pay it yourself, and 99% of the time it works.
If its under warranty, then make sure they foot the bill. If its not under warranty, then (sorry to say) they have no legal obligation to cover it unless the government forces them to issue a recall.
If its under warranty, take it to another dealer with a sob story about how "the other dealer wouldn't honor the warranty." They will kiss your butt in the hopes of making you a new satisfied customer and you'll have a better chance of getting it repaired.
Next time you're in the service department and you look at those awards on the wall from the car company, know this: some of those awards for "service excellence" are based on a service department's ability to convert warranty work to customer-pay. Seriously. We used to have weekly meetings on how to convert more customers so we could win more awards.