Yup, sounds exceedingly non-British to me.
Regarding being a Crown dependency, it does not make it british, it is simply a result of the unified function of King of England and Duke of Normandy.
Now I will be intellectually honnest, I was approaching the issue from a political angle (because I have always dealt with this aspect for work), and under this framework I am right. However, from a geographical standpoint, there is an argument, it is sometimes included to the British isles, sometimes not. Since the government of Jersey considers itself as part of the British Isles, I guess saying they are British is acceptable. Mea culpa.