I can understand that you could get 'caught out' on doing your own oil changes by the dealer if you were to change your engine oil for the first time before the dealer does and thus voiding your warranty.
I say this, because as jrkitching posted in another thread and which I subsequently noticed prior to my own car going in for a first service only two weeks, the oil filter fitted to a new car, is a factory fitted filter, with a different part number unavailable I understand from the dealer.
My own European 500 now has a Fiat original spec oil filter available from all Fiat dealers, not the factory spec fitted one. Therefore, I could hazard a guess that I could now, should I wish to do so, safely carry out all my own oil/filter changes using Fiat oil and filters without the dealer network suspecting a thing. As things stand, whilst my vehicle is under warranty, Fiat will be servicing it anyway, but once the three years are up, I'll start doing the services myself.