Well, they should, if they're going to honour their own policy. Really it all depends on two things. Firstly the factory which has the ultimate say and its for this reason that it is very important to make sure ALL the required information is provided and that its provided in the right way and then secondly the dealer has to be interested enough to try and do the right thing.
At the end of the day there is little to no incentive to try and chase up warranty on other people's problems. You don't get paid for warranty work, you get a set amount of hours decided by the factory for the repair and nothing for the diagnostic time. The hourly rate is about 1/3rd to 1/2 of real shop rate and it isn't given to you as cash, its given to you as a 'Credit' against your parts account! You can understand why shops are reluctant to take on what are perceived as 'Other Peoples Problems' and in fact its exactly the reason I'm no longer an 'Official' service agent for Moto Guzzi.
I knew with the new importer I'd just be getting bikes sold from big 'Box Shop' dealers in the major metropolitans which would have had little or no pre delivery done and any that had been touched would of had the assembly done by the work experience kid with zero supervision. They's then be waved on their way and when it turned to shit they'd phone up the shop they bought from who would say I was their nearest service agent and I'd be overjoyed to fix their shit! So I end up having to deal with an angry, pissed off customer and listen to him telling me how Moto Guzzi are shit and anyone who works on them is a c*nt! Anyone who knows me knows exactly how that's going to work out for them......