So......it would appear there is a legitimate concern about serious engine issues upon detection of below minimum or loss of engine oil pressure that in some cases require an "emergency shutdown" of the ailing engine.
The procedure is different between Aircraft.....single versus twin engine owing to the idea of shutting down the only engine running creates its own dire emergency if done in flight.
Also, it is appears other considersations come into play in the decision to shut down an ailing engine.
This thought of "immediately" shutting down an engine bears some review to determine exactly what "immediately" should mean.
Rushing into carrying out an Emergency Procedure requires careful consideration as well because doing so might make a bad situation much worse.
We have to get back to the reality of Aviate, Navigate, Communicate to guide our actions......but most importantly we must (imperative tense) "THINK" about what we are doing to ensure we consider all of the factors before taking action when things start going wrong.