While I basically agree, one of the arguments in the episode (as I remember it, it's been a while) is that since we ship it away, we don't see the negative results of our lifestyle choices, making the problems created easier to ignore.
Also, they argue that modern landfills _can_ be pretty damned "green", capturing the heat/gases created and using them to generate power.
But since we've prioritized and financially incentivized recycling (shipping everything somewhere else) we haven't prioritized responsible ways to manage waste locally and once our waste gets rejected we'll likely to be playing catch-up.
The problem is mis-representing what's in the shipment.
(There's probably a lot of plausible deniability in the system. People throw a lot of trash into recycling bins for lots of reasons, including ignorance or laziness. Trash companies don't take responsibility to make sure that's what's in the bin is actually what's supposed to be there.)
Read the article. There's dirty diapers mixed in with so-called "recyclables."
It's a whole bidirectional cascade of misrepresentation I think: every time the materials change hands, the output side passes on the quality/purity promise from upstream, but more optimistic within an almost reasonable error margin. In the same transaction, the input side passes on the responsible handling promise of their downstream partner, but more optimistic, within an almost reasonable error margin.
How many intermediate subcontracting steps would it take to allow the original source tho pay for (supposedly) perfectly clean full reuse recycling of a toxic mess, and the final sink to dump (supposedly) perfectly harmless materials into the sea?
Especially when ships and containers are going that way empty anyway.