Laws of physics forbidding it is understandable. We may likely never see the development of FTL because our understanding as we know it would see it impossible to do due to its strange implication about cause and effect.
And they used other words next to the unquoted impossible in the article itself like "deemed by scientists to be next to impossible". Context matters.
The part I'm confused about is how it talks about all of these 60s rockets that close the cycle but aren't as efficient because they mess up the mixture in the combustion chamber, but shouldn't the injectors be tuned for the excess fuel/oxidizer from the get go? It doesn't seem like you should be exhausting unburnt fuel/oxidizer if you have it tuned correctly.