Ok, after discussion, it seems that the best solution is to maintain the links even if the action is not doable: the user will get there an information message, as long as needed.
Plus such links will be lowlighted in a specific manner so users can easily understand they do not have access to this action.
This behavior should be standard.

It does not mean we have to print every action link possible everywhere: it means we have to print every action link that could reasonnably be available to a lambda user (no need to print the Administration bar to non-member, non-admin or not-logged in, for instance... -- but posting item should be)