I agree that they chose to be offended. The following is a story of how people could (and IMO, should) behave:
When I moved into my first apartment, it was in the basement of my landlords' house. They were Muslim. That first Christmas, I agonized over whether or not I should give them a gift. And I agonized over the card to go with it, once I decided that I was going to give them something. I very carefully chose a card that said 'Happy Holidays' and not 'Merry Christmas'. Not only did I get a gift back from them (that I still use 22 years later), the card they enclosed said 'Merry Christmas'.
For the next 8 Christmas I lived there, I gave them a gift and they reciprocated. I still send them a card now that I've moved away. When I still lived in the area, I used to visit and take them some baking. And she gave me some of their's that had been made for Ramadan, which was still close to Christmas at the time I left.