I'd have to agree almost entirely with Niney.
There is really no need to use a webcam. If you like using your webcam and such, then that's great I guess. If people ask you to show your webcam and you don't want to, then you shouldn't do it. One thing I don't like about the italki chat system is that people can show you their webcam without asking you first, which I don't like.
If people try to convince you by saying they don't believe you, I would just let them not belive you. Your picture has nothing to do with learning language or culture.
Personally, I don't own a webcam, so that's not really an issue for me. I use my mic with people I know and have chatted with a while and trust them. Not with people I just met though.