I agree with your concerns. It would also be significant as to how the CEO introduces the "friend" if at all. In business meetings it is usual to introduce everybody to everybody and indicate in what capacity they are attending the meeting. So a silent shadow would raise eyebrows at a minimum.
Agreed. Before my shadow day I get the CEO to send a quick email to everyone in the company introducing myself, why I'm in the office etc. This seems to work well.
Interesting, could you help me understand what type of important meetings you're talking about and why you would not be comfortable?
I haven't experienced people having a problem with me observing their meetings before, in fact most people are really happy for me to learn from their meeting. I understand some meetings could be difficult though eg. HR related