In "Simulation without the artificial abort: Simplified proof and improved concrete security for Waters' IBE scheme", Bellare and Ristenpart present a new proof for Waters' IBE scheme that does not use the artificial abort technique. As in the original proof, the authors define an adversary $\mathcal B$ that breaks the DBDH problem using an adversary $\mathcal A$ that wins the IND-CPA security game of Waters' IBE scheme.
I'm studying the proposed security proof, and in page 10 it states the following:
We note that our adversary in fact never aborts. Sometimes, it is clearly returning incorrect answers (namely $\perp$) to $\mathcal A$’s queries. Adversary $\mathcal A$ will recognize this, and all bets are off as to what it will do. Nonetheless, $\mathcal B$ continues the execution of $\mathcal A$. Our analysis will show that $\mathcal B$ has the claimed properties regardless.
I don't understand how if adversary $\mathcal A$ can detect sometimes that the answers to her queries are incorrect, this does not imply that $\mathcal B$ cannot use $\mathcal A$ anymore.
In general, what is the implication of an adversary detecting incorrect answers from the simulator, assuming that this happens with non-negligible probability?