OP is correct. You've quoted the general language around move semantics but unique_ptr itself has a stronger gaurantee.

From 20.7.1

  Additionally, u can, upon request, transfer ownership to
  another unique pointer u2. Upon completion of such a
  transfer, the following postconditions hold:

  — u.p is equal to nullptr,

unique_ptr isn't what's unsafe here. Null pointers are. The difference, admittedly, is mostly semantic. There is nothing undefined about using a unique_ptr after moving unless you use the internal pointer in undefined ways.