I'm with basil there. Plus, every single car I ever bought from a dealer (including this one) has that fantastic acronym FSH in the advert.... some have half the MOT (with a "missing" advisory sheet - it's a very good thing that it's all on one page now!), some have the very first servicing from the first 2 years and nothing more, some have a recent stamp from the dealer's mate and nothing more.... I've yet to see a car with FULL service history - although my Brab comes closest with just a couple of minor gaps.
I suppose the only thing about your car that would support a dealer service history at its age is the low mileage, and the fact you hardly drive it, so at some point in the future it could be a shining example of an older car.