What if....Shizuko herself was adopted by her parents after she time traveled to the present future as a younger child, and thus wouldn't have remembered it being so young. That would explain why her parents are so willing to take in a complete stranger carrying a deadly banned weapon in modern Japan. For all they knew, he could have been yakuza.
Also curious about the doctor's backstory and how he came to hate the police in a generally peaceful Japan. Although probably not all that difficult to imagine a decent reason, given how many times police have given people a reason to resent them in recent times.