Robust design: S or phi?

[Claudio]

I read and read again chapter 15 of the MARK book, and a question comes to me. At the end of page 15-5 one can find:
"In the absence of extra information (specifically, dead recovery data, or the equivalent), partitioning apparent survival φ into component elements S and F is not feasible using the classical robust design (which is based entirely on live encounters at a single location). We will deal with extensions to the classic robust design (including use of extra information such as dead recovery data) later in this chapter."
Basing on the preceding statement, there is no reason to use S instead of phi. Consistently, in table on page 15-10 phi is used. On the contrary, through the rest of the chapter S is used, as well as when using MARK for the robust design.
Thus, my question is: does CRD assess true survival S or apparent survival phi?
Later in the chapter there is no clear solution to this problem. I understand the similarity between gamma and psi, and this should lead to S. However, I would like to get reassurance on this issue.
thanks in advance
Claudio