YMMV
I've not had any problems having my cars serviced at a different dealer than the selling dealer.
However, back in the last millennium, my Dad did have an issue with the local AMC dealer who flat-out told him the since he bought his car at a different AMC dealer, he should take it back there for the warranty work the car needed done. One call to the Zone Manager and their attitude did a 180.
I've not had any problems having my cars serviced at a different dealer than the selling dealer.
However, back in the last millennium, my Dad did have an issue with the local AMC dealer who flat-out told him the since he bought his car at a different AMC dealer, he should take it back there for the warranty work the car needed done. One call to the Zone Manager and their attitude did a 180.