I didn't read their idea, but you wouldn't ever need to go faster than the speed of light for this to work -- just approaching it infinitely close would be enough.
Sure it might take a hundred million years for your journey from an observer watching you on earth, but thanks to time dilation, it could still be less than a lifetime for the person on the ship
Well then how do you get to the parts of our universe that are receding at a speed faster than light due to space expansion?
I'm not nearly as comfortable with relativity as I'd like to be, but too much in this hypothetical "woahdude" scenario ends up being a logical roadblock to me.
Sure it might take a hundred million years for your journey from an observer watching you on earth, but thanks to time dilation, it could still be less than a lifetime for the person on the ship