That's true. The FAA had a stellar record as a certification agency, which, it can be argued, they fucked in three days (sure, the hole history of this sad debacle is more complex. But by keeping the plane in the air longer than any other certification body in order to not hurt their buddies at Boeing they completely ruined their reputation, which was built in decades of good work).
I can't imagine that any responsible certification body anywhere trusts the FAA anymore without a complete and significant shakeup.
It's a sad story, really.
EASA.
FWIW, the Brazilian regulator (whose name I don't remember...) did not rubber-stamp the FAA's type certification of the 737 MAX, and required some differences training for MCAS, IIRC.
And, yes, the Ethiopian Air pilots apparently did follow the procedures initially, flipping the Stab Trim Cutout switches, but did not manage to recenter the trim manually (via the trim wheel), so apparently re-enabled electric trim, and then let MCAS drive the trim even further down to their doom. :-/
This is unlikely to change. It’s expected that some changes will occur at the FAA. Certifying an airliner is also a prohibitively expensive undertaking, which is part of the reason for this mess in the first place. It would take years even to train enough personnel to duplicate all those efforts.
I wonder if the European agency (don't remember the name) will stop trusting the FAA from now on and do their own tests. I'd thank them for that.
(According to what I read here, the European agency doesn't do exhaustive tests because they mostly trust whatever the FAA says; maybe that's false)