No, I'm not going to watch the linked video to find out whether he's really answering my question or not. Tell me why I can't synchronize two atomic clocks that are right next to each other, then put one in a car and drive 1000 km away. Tell me why that won't allow me to correlate departure and arrival times well enough to answer the question.
You are being rather demanding, but I'll bite anyway.
When a synchronized clock is accelerated, it will experience time dilation as compared to the stationary clock; they will no longer be synchronized. You might think: ah, I'll just correct for that using relativistic calculations. But you'd be wrong again because Einstein explicitly states that everything in his theory assumes that the speed of light is uniform.
