How often do Dutrow and Prado ship to Suffolk? About as often as Barclay Tagg, or any of the other trainers or big name riders in that race do. A total non-factor in my opinion.
OW had his brains kicked in, as you say, in prior stakes attempts, but he did win the Holy Bull, and for me, the trainer change makes that all obsolete once he ran huge for the new trainer.
All that said, the exacta was the value in the race, obviously not the win pool, and but for a head, I would have lost...such is racing.