This is mostly right. The governments can set quota, for instance say that Japan had a Trade deal with the US for 250,000 tons of corn, then that would mean that Japanese buyers could bring in up to 250,000 tons of US corn. This would result in the US market trying to find buyers to take that much and if they couldn't, then they'd not be able to send in 250,000 tons. Now in this case that seems to be the issue with China, i.e. it simply didn't have the markets for the set quota. Japan could take more corn, if it's businesses are willing to buy it, and the Government is willing to increase the quota. It seems that the Japanese Government is willing to up their quota, allowing more corm to be imported, but the US producers will still need to find the market in Japan to actually but the increased amount of corn available or they will be in no better position than they are now.