I think the problem is that jw's do indeed see themselves as witness of jehovah, they see it as a calling or give great meaning to being one of the few who are 'privileged' to supposedly give witness about or to God. They say the phrase 'I am one of...." with much reverence and all seriousness. The few times I have heard a jw say the phrase you would think by just saying the phrase to a non jw it will somehow shower down blessings on them or something.
To the rest of the world? you are 'a jehovah's witness' just like someone is 'a Baptist', 'a Catholic' and so on. I shall refrain from what people really call them and leave that to the comedians!