Original fictional reset. No mail was sent. No account exists.

Rule for token RIVER:
  random value stored by the server
  expires at 16:00
  valid until its first successful use
  after that success the server marks it used

Worked trace, token RIVER:
  15:40 first use succeeds and sets a new password
  15:41 second use finds the used mark
  Decision on the card: the second use does not meet the rule

Contrast card, token POND, not used in the question:
  the same value is accepted on every visit until 16:00
  the card marks that pattern as reusable