[ThrustVectoring]

The key thing is that if your old employer is sending out demand letters, you have to go through expensive legal proceedings to clear the encumbrance on employing you. Your new employer has a letter stating that they have to either immediately terminate your employment or get sued - even if they will win in the eventually legal proceedings, lots of places are not willing to get sued over it. Some won't even be willing to pay a lawyer to figure out whether or not the suit has merit.