Ask HN: Do you make your CV public?

In my corporate life, I have noticed that most of the senior/executive staff are quite protective of their CV's and profiles.

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?