Aspenite (OSB) is used quite a bit in domestic crates and I am quite sure there are companies using it overseas. However you are right. The aspenite will tend to soak up moisture especially out on the ocean. It does not have to even be particularly wet weather but there is enough salty moisture in the air that your crate basically becomes somewhat weaker as it soaks up moisture during the trip. Don't forget these type of shipments are usually over a period of a month to 2 months from the time it leaves your facility and then it is picked up and handled atleast 6 times or more before it gets to the destination. I have seen people try to shrinkwrap the crate afterwards to protect from moisture but again that usually creates moisture between the wood and the plastic creating more problems.
Better to use wood or plywood for sure.