That's an interesting theory Brad, if developed countries are contributing to the 'plastic waste in the oceans' problem to any extent, it is probably through the practice of sending plastic waste abroad for 'recycling'. If the recyclers in developing countries can't make use of all the plastic waste they import, they may just dump the surplus in rivers.
After doing a bit of research, I found that China is the world's predominant recycler of plastic waste:
The EU apparently exports 87% of the plastic waste it collects to China, including Hong Kong. But China has recently announced a policy where it intends to cut back substantially on importing foreign waste from next year onwards, and will recycle its own domestic waste instead, so much of the plastic waste collected in developed countries may have nowhere to go. If China recycles its own plastic waste, that will obviously keep some of its own plastic waste out of the rivers.
One country I was expecting to be a big contributor to the 'plastic waste in the oceans' problem was Mexico, but that doesn't seem to be the case. Mexico is notorious for having a litter problem, as discussed in this US newspaper article from ten years ago:
Rubbish gets thrown into rivers in Mexico (the article mentions an incident where the Grijalva River got clogged with trash in a narrow gorge), but it may be that the geography of their rivers is such that not much gets carried into the sea.