Ricardian vs Non-Ricardian policy identification
I think you're misreading what Sala wrote. The first sentence in the image you linked is just saying that in the worlds where either Case 1 or Case 2 occurs, the response of $b_t$ to a shock in $s_t$ allows us to differentiate between Ricardian and non-Ricardian regimes since there are no identification issues. In other words, if either the Case 1 inequalities or the Case 2 inequalities hold, then we can be confident that we have identified a non-Ricardian regime from a Ricardian regime.

According to Sala, it seems that we cannot as easily identify Ricardian regimes from non-Ricardian regimes in Case 3 due to identification issues related to co-movements in real debt.