The traditional problem left to us from Boltzmann's debate with Loschmidt, as I understand it, is that since the fundamental dynamics are time symmetric, statistical mechanics makes the same predictions toward the past as toward the future. Not only is it overwhelmingly probable that present states evolve toward equilibrium, it is also overwhelmingly probable that present states evolved from equilibrium states. The latter simply doesn't happen, however. Roughly put, the traditional problem of time's arrow therefore amounts to explaining this faulty retrodiction away. The traditional problem should be distinguished from Price's.
Price wants to explain why entropy was ever low in the first place.
This might be taken for the traditional one, for it too originates from the fact that entropy was earlier lower. Given the right sort of non-TRI dynamics we would know why entropy was earlier lower, in the sense that we would know entropy always increases. That is, we would know why entropy doesn't increase toward the past as well as toward the future, which would answer what I'm calling the traditional problem. Yet we still wouldn't know the answer to Price's worry about why it was ever in nonequilibrium in the first place. I don't know that it is.