There seems to be basic mis-understanding on ETOPS statistics.
An inflight shutdown in any phase of flight becomes part of the ETOPS statistics used to determine the suitability of an engine/airframe for ETOPS operation.
Futhermore, it doesn't even need to be on an ETOPS airplane. A CFM56 shutdown on a non-ETOPS 737 becomes part of the CFM56/737 database used to determine CFM56/737 ETOPS eligibility.
Engine shutdown rates are monitored very closely by national certification agencies.
There have been instances where national authorities have removed ETOPS approval for their national carrier when the carrier's shutdown rate crept above the shutdown rate requirement.
This wasn't quite right as the shutdown rate requirement is supposed to be based on the world fleet data.
Kind of reminds you of Lake Woebegon where all of the children are supposed to be above average.