Given that it was probably quickly deduced that a round trip to the somewhere was being attempted, they might have had a few minutes to grab a few essentials. So, yes, I think you're right. This is the simplest explanation and it is consistent with flight.
There's another angle to this though that deals with the psychology of the "barter" made between these two. What was their role and relationship vis-a-vis JEW? I need to think about that, too. That could affect how quickly he left. For other reasons I think S1 did go to IL and both DR and S1 had a common, familiar territory down there. They attended grad school there together some years before.
~ svh