  A recent quantum protocol for counterfactual communication [Y. Aharonov and
L. Vaidman, Phys. Rev. A 99, 010103(R), 2019] relies on post-selection to
eliminate the weak trace in the transmission channel. We show that the
post-selection in this protocol also eliminates the flow of Fisher information
from transmitter to receiver. However, we also show that a classical
communication protocol with post-selection can be counterfactual. Hence, we
argue that post-selection should not be allowed in genuine counterfactual
communication. In the quantum counterfactual communication protocol, the
probability of discarding an event by post-selection tends to zero with an
increasing number of ideal optical components. But the counterfactual violation
strength tends to infinity at a faster rate. Consequently, the quantum protocol
is not counterfactual proper.
