Even more, if they are members of linkedin, they usually only present their job titles with no further description of role or responsibilities. This would seem to me counter-productive as a potential recruiter would be less likely to find their profile using a generic search.
Personally I would have greater trust in a public CV because my feeling is that the respective person would be less likely to lie or embellish facts in a CV that be seen by their immediate peers.
Is your CV public or not? Why? Do you fill in your complete linkedin profile or just job titles? Why?