It's not a lie, just an oversimplification.
In some media such as glass, different frequencies of light travel at different speeds, a phenomenon called "dispersion". In some media, such as extremely carefully prepared clouds of ultra-cold caesium atoms, you get "anomalous dispersion". In media with anomalous dispersion you can get different frequencies to travel in such a way that they interfere to make a hump that "moves" smoothly along at any speed. But, crucially, the laser beam has to be already propagating all the way along where you want the hump to appear, and must be carefully pre-prepared.
This analogy is not perfect, but have you ever seen a Mexican wave in a sports stadium? One column of the audience stands up, and sits down as the column next to them stand up. A wave propagates around the arena like this. Its speed depends on how long it takes your average person to react to the person next to them moving and to stand up themselves. But, instead of doing it spontaneously, you could give everyone a watch and tell them: column 1 stands up at 12 o'clock, column 2 stands up at one quarter of a second past 12, column 3 at two quarter seconds past, and so on. The wave would go faster. And faster if you used tenths of a second instead of quarters, or hundredths of a second instead of tenths. Eventually, if you carry on shortening the time interval, the wave speed would exceed the speed of light (in principle - in reality, the precision necessary is well beyond human reaction capability). But that's fine because nothing is moving or communicating faster than light - the people are just executing pre-planned instructions to make a hump that "travels" while nothing is actually traveling in the direction the wave "moves".
This experiment is enormously more sophisticated than that, and it has highly technical implications for how one should talk about the speed of light in media with anomalous dispersion. But it's no challenge to relativity because it's not very different from the timed-Mexican-wave phenomenon.