To me, the song was funny! I had never met any of my grandparents, at least, not while I was old enough to recognize them, and "Grandma" was pretty much just an intellectual concept, not especially tied to any concrete reality. (Think: the Democratic Party!)
My ex-wife, on the other hand, had lived with grandparents for a while, dearly loved her grandmother and it was in an entirely different connotation that she heard the word "Grandma". For her, the song was not as funny! She had a different perception of the word "Grandma". "Grandma" was a real person.
Which, reminds me of one of my favorite college texts, Sleepy Sam Hayakawa's Language in Thought and Action. The map is not the territory. Language, the map, is not a perfect representation of the territory it describes. It leaves...room for error in communication. Not only about grannies getting "run over".
When you consider that what I say is not exactly what I think I said and what you hear is not exactly what you think you heard, it's a wonder anyone understands anybody at all.
So we rely on secondary clues, on context, on facial expressions, on tone of voice...anything to make it all make sense. Owen Wister's Virginian said, "Smile when you say that", because an insult offered with a smile has an entirely different connotation that one given with a sneer.
The Internet, credited with giving us near instantaneous communication, can be very bad for that very reason. It is stripped of clues and inflections that might otherwise illuminate the meaning of the words. I can think of several examples where I offended someone or someone offended me by something that could be taken more ways than one. Adding a smiley face or a frowny face is a poor substitute for hearing the sound of one's voice. (Was that "sarcasm"? Was he being sarcastic? I couldn't tell!)
So, if you're offended by "grandma getting run over by a reindeer", you're probably looking at "grandma" in the concrete rather than the abstract. And if "Grandma in the concrete" gives you images of cement overshoes, well, then... welcome to my world!
In whichever language you call your own, however you perceive it, may you and yours have a happy, reindeer incident free holiday and a prosperous new year. Merry Christmas!