The idea that a person is killed and copied whenever they use a transporter has been around for a long time in offscreen lore. I read about it in the early novel Spock Must Die!
Regarding the transporter being able to make two equally valid versions of one person, there is precedent in Trek. In "The Enemy Within", neither half of Kirk is the whole package...each possesses qualities that are integral to his personality. Both are equal duplicates physically, however. There was no such clear division between the Riker duplicates, other than the circumstances under which they'd lived after the accident.