It could just be that he personally gets carryover from it while others don't. From what his 5/3/1 books say, he isn't into the kind of benching you are talking about. That's more like Louie Simmons and Dave Tate's style, which seems to work for equipped lifters only. If you need to row the bar to your chest without a bench shirt on then you have some serious mobility issues.
One guy told me that he did a cycle of the Sheiko 4 day program and started to get shoulder problems after because there is no overhead pressing. He later added in some light dumbbell pressing and was back to normal. What I heard is that there is a rotator cuff muscle than can get shortened from a lot of benching and no overhead work, it doesn't seem to be an issue for some people though.
Overall it's a good exercise, but if your goal is to bench more then you need to bench more. I see some guys looking for programming advice and they bench once a week and press twice.