She makes two arguments, both based on Special Relativity.
The first is that the energy required to accelerate a massive object to the speed of light is arguably not infinite.
When v=c in the equation, the expression becomes singular.
IOW, no longer valid Physics, just like anywhere else infinities arise.
( alsoexplains how mass is mostly binding energy, and the workings of the Higgs field )
The second, also using SR, using FTL travel, or communication, to send information elsewhere, then back to yourself in the past and violate causality, seems to disappear when GR is considered, as the co-moving frame estabilishes an entropic direction to the future and makes sending information back to your past self from elsewhere, impossible.
The direction would be from your past self to elsewhere, not the other way around.
I enjoy her humor, but SoL invariance ( and the reason why all observers measure the SoL to be the same, why you can't catch up to light, and why it takes increasing amounts of energy to approach the SoL barrier ) is the footing of the foundation of SR and GR.
Without it much of modern Physics crumbles to the ground, nd we know that both SR and GR have been immensly successful.
Maybe, as Sabine mentions, Quantum Gravity will redefine the singular points where v=c just as ( we hope ) it will for the singularity of Black Holes, leaving the rest of SR/GR unchanged.