Enforcing race safety without giving up on mutable objects, would be a best wording of it.
The problem is simple. Let s imagine you have a mutable map M, and actors A1 and A2. Actor A1 sends a message to actor A2 containing M. The question is, are you running any risks?
The idea of the paper, if I understood it correctly, is to improve the type system so that you can guarantee that A1 will not reuse M after it was sent to A2. You use a mutable data structure, but you ensure, through the type system, that it can only be accessed at one point of the code at a time.