While I suspect there might be some shenanigans, just look at how e-waste is illegally dumped on some countries for example, from many articles I've read in the past, a lot of plastic waste in the pacific is due to developing Asian nations and their growth in consumerism. They're buying more and more stuff, but don't have the facilities to properly process their waste.

This article gives a decent overview. Basically it's a combination of large amounts of waste, inadequate facilities to process them, and lack of oversight and enforcement of regulations.

There's a really good article that I'm trying to find that illustrates a lot just through milk cartons. When I find it, I'll share it. You'll probably find it interesting.

Edit: Here it is! The blight of Tetra Paks covering Vietnam's beaches and towns

Milk consumption in Vietnam has almost doubled in the past 10 years, as the dairy industry shifts its focus from “saturated” western markets in favour of Asian expansion and is now valued at $4.1bn (£3.1bn). But one of the biggest beneficiaries of this growth seems to be the dairy industry’s principal packaging supplier, Tetra Pak. Last year, 8.1bn of Tetra Pak’s individual cartons were sold across Vietnam. Yet a comprehensive country-wide recycling programme is yet to be implemented. Now, as cartons pile up on beaches and in landfills up and down the country, that’s having a devastating effect on the environment.

The whole article is interesting, because it illustrates a lot of the roots of the problem with a single product.