Hi Ignacio, and thanks for your answer.
So, I made a mistake with this bug and misunderstood what was happening :
Here is a new bug report :
In 1.6.2, an user without "can manage all contacts" rights can't create a new contact : an error message "you don't have permissions to do that" appear... despite he can create a new company.
Do you want me to create a new forum post about that , linking to this one?