They don't need to sync for it to be a serious weakness in a cryptosystem. If a system using Khoth's PRNG sends out a billion encrypted messages in its lifetime, then an attacker with the PRNG key needs less than 2^30 tries to decrypt a message sent at an unknown point in that sequence -- a large number, but more than manageable when you consider that a PRNG with a period of 2^80 would be considered weak in the crypto world.