do we really know, WITH ABSOLUTE CERTAINTY, from a reliable source that the crew actually shut down ANY of the engines or did they land with both engines running sans cowlings?
No, we don't have any conclusive evidence,
AFAIK, that the crew did or didn't shut down any engines.
But if an engine
was shut down, we known it wasn't No1 (or if it was, it was restarted before the landing, which is a tad unlikely). How do we know? Because we have video evidence of the deployment of No1 thrust reverser during the landing rollout.