Sylvan is denouncing his invention and admits to not even owning a Keurig machine. Besides the expense compared to a normal drip coffee-maker, he is also concerned about the K-Cup containers and their lack of recyclability.
" 'No matter what they say about recycling, those things will never be recyclable,' Sylvan said. 'The plastic is a specialized plastic made of four different layers.' "I admit again, that I never it gave it much thought, but the package is pretty complicated. The cups have to protect the ground coffee from oxygen. That's easy for the top of the cup which is a piece of foil, but the plastic cup itself requires an oxygen-barrier plastic, such as ethylene-vinyl alcohol (EVOH) or polyvinylidene chloride (PVDC, aka Saran [*]). And that's where the problems start. Barrier plastics are great at being barriers, but seldom perform well on their own and so they are usually incorporated into multilayer films or sheets such as in this case. And hence the concerns with recyclability and why they are marked as plastic #7 (Other).
"....a specialized plastic made of four different layers". That's odd, because it isn't odd. To be clearer, that's odd because it isn't an odd number of layers. Barrier plastics are usually more expensive than the base plastic, so thin layers are typically used. This can lead to problems with holes in the thin layers, so to address that, typically 2 or more layers of the barrier plastics are used with the thought being that the odds of two holes in the barrier layer being in the same are other is remote. The construction would then be base/barrier/base/barrier/base - which is an odd number of layers - 5. It can get even more complicated when the base and barrier don't stick to each other. Then a tie-layer can be coextruded, which further increases the number of layers. But even if the barrier plastic is still only used once as in a base/barrier/base construction, you still have an odd number of layers - 3. I'm not sure how you could effectively have a 4-layer construction.
I'm not sure what plastics are used as the base in the cup and in the filter (the patent is expectedly plenty vague.
I would encourage you to read the entire article as the bottom-most section gives an interesting perspective on how the Keurig machines and K-Cups might not be as bad as we might think. They can unexpectedly reduce waste in other ways that we accept without question. The author describes the issues very well, so it's pointless for me to try and repeat them. But you will see that the reaction to K-Cups is very much like the reaction to disposable water bottles. By focussing on just the delivery device right before, during and after the consumer uses it, you miss out on the bigger picture. An optimized solution is never found by optimizing just one part of the problem or by optimizing each part separately, but instead by looking for a global optimum. That such global optimums may appear to be non-optimized in a local area can be confusing at times.
[*] Saran was the tradename that Dow first used when introducing this material as a household plastic foodwrap. The product line has since been sold to S.C. Johnson who kept the tradename, but changed the plastic to a chlorine-free alternative.