I went to someone's twitter profile & it was public (I could read all the tweets) I logged into twitter and went to follow them but it said their tweets were protected (although I could still see their images, who they were following etc). There was also no padlock symbol next to their name.

Is it normal for someone's profile to be public to non logged in users but blocked to logged in ones? As an aside through my business twitter account (which they follow) everything is 'normal' even though I'm not following them through there either.

Seems a bit odd as I was under the impression your twitter account was either public or private, there was no option for selective privacy?