You don't need to know quantum physics to know this is BS for most cases because FTL is about
- manipulation of space-time
- preservation of the ship during travel
- hence, the fundamental property of matter of being noncommutative cannot be broken
So unless the method of travel does not include or require the body to be broken up in the first place for "travel" quantum entanglement is impossible beyond the Planck scale.
The metaphor of being everywhere in the universe if you are fast enough is only to illustrate so people would understand the problem. It's abstract at best and doesn't mean it's exactly like that (definition of metaphor).