They were at FL380 which is damn near the ceiling for the Ejet at that gross weight (assuming they were carrying through fuel). Speaking from experience here, they would have been near coffin corner but not right at the edge. You do get the PLIs really quick at that altitude so plenty of time to react. Plus, it was daytime. Personally I think WX is unlikely here.
It sounded similar to the B737 problem of the rudder going hard over as they were commencing initial approach. A sudden partial or total loss of control could explain a ROD of 6000fpm and no communication from the crew
That's my two cents worth, although mind you, I REALLY hope I am wrong on this one.