The chemicals that went up in flames in Beirut’s deadliest peace-time explosion arrived in the Lebanese capital seven years ago on a leaky Russian-leased cargo ship that, according to its captain, should never have stopped there.

“They were being greedy,” said Boris Prokoshev, who was captain of the Rhosus in 2013 when he says the owner told him to make an unscheduled stop in Lebanon to pick up extra cargo...