That's correct indeed, you should have no problems at all. In fact, when going through passport control before trains to E gates, I don't even show them boarding pass - only passport or ID card. Its not that quick sometimes, especially if there are delays at passport control, but on a 3 hours layover I would certainly do that. Another option is the lounge in D gates, for which you don't need to take the train. But the lounge is much worse, only makes sense if the queues at passport control to E are crazy.