The problem only arises when considering energy eigenstates, which are completely delocalized. One of the tenets of the equivalence principle is that the equivalence between gravitational systems and accelerated frames is only true locally. All that the equivalence principle states is that there is a neighbourhood in any point small enough such that the physical systems are equivalent. But an energy eigenstate will be dependent on the physics outside any such neighbourhood. Because of that, eigenstates being highly delocalized states, do not need to satisfy the equivalence principle in any way
A more detailed explanation would be as follows: The transformation induces a Hamiltonian on the accelerated frame. The equivalence principle says that if the locality is small enough, you can't do a measurement inside the locality that will tell me if I'm in a gravitational potential or in an accelerated frame. But, by definition you can't make perfect momentum or energy measurements inside such locality because your locality has an extent in space, so the position can't be outside of that extent. Hence no possible measurement inside the locality can tell apart extended eigenstates of energy or momentum. If the packets are narrower than the width of the locality, the equivalence principle should hold. If the packets are widers than the locality, the equivalence principle should NOT hold