Why is a threshold determined for Byzantine Fault Tolerance of an “Asynchronous” network? (where it cannot tolerate even one faulty node)

In following answer (LINK: https://bitcoin.stackexchange.com/a/58908/41513), it has been shown that for Asynchronous Byzantine Agreement:

“we cannot tolerate 1/3 or more of the nodes being dishonest or we lose either safety or liveness.”

For this proof, the following conditions/requirements has been considered:

  1. Our system is asynchronous.
  2. Some participants may be malicious.
  3. We want safety.
  4. We want liveness.

A fundamental question is that:

With considering the well-known paper titled: “Impossibility of Distributed Consensus with One Faulty Process” (LINK: https://apps.dtic.mil/dtic/tr/fulltext/u2/a132503.pdf)

showing that:

no completely asynchronous consensus protocol can tolerate even a single unannounced process death,

Can we still assume that the network is asynchronous ? As in that case the network cannot tolerate even one faulty node.