Under what conditions is it permissible to pump machinery space bilges directly overboard without processing by an oily water separator?

Correct Answer: Option B — When presented with a flooding emergency.

MARPOL Annex I and 33 CFR Part 151 strictly regulate oily water discharges. Bypassing the oily water separator is only permitted in extreme circumstances, such as a flooding emergency where the safety of the vessel and crew is at immediate risk, necessitating the rapid removal of water to maintain stability.