I'll be the first to admit that Americans can be arrogant, but this language would be an example of European arrogance, *if* it were spoken by someone from there. I don't have a full list of places named Cambridge, yet I'm to assume they are all named after the one in England. This is kind of like just expecting everyone to assume "Brest" means the city in France.
When I hear Cambridge, I think of Massachusetts. I grew up in Massachusetts, went to school for a year in Boston, and my daughter lived in Cambridge for a while. Even with all that, I can't muster the energy to find it irksome when someone just writes "Cambridge", even though they mean the one in England.