Not true. Musk said they weren't ready to launch yet anyways, and that they expected to be ready around the same time they expected to get FAA clearance. So it's not holding things up yet. And it might never.
It would not be at all surprising if they did not get approval for anything like the launch cadence from Boca Chica that they had projected, and need to fall back on Florida and ocean platform launches.
The delay to get that stuff ready might give them time to actually work out bugs, without them being treated as failures. And, there is little doubt those will work just as well, although standing that stack up on a floating platform will be an impressive achievement. Boca Chica will still be able to do tests. One wonders if they will deliver completed vehicles to the real launch sites by ("test") launching from Boca Chica. I don't think you need a Starship on top to launch the booster, although a cone hat seems advisable.
I was just trying to imagine a booster delivery flight path. I'm assuming orbital otherwise FAA has appropriate concerns.
So north of Cuba, achieve orbital speed for one orbit, de-orbit burn to re-enter aiming past Florida, and then landing burn to get you back over Cape Canaveral?
Is it that straight forward? Would that be allowed? Would they need to dog leg to avoid flying over mainland USA?
Maybe an unladen Starship could make such a hop by itself. If not, a booster could assist on the first leg and come back.
On that note, I recall reading somewhere that the top part is at least in theory SSTO-capable without payload.