The agent is correct; Hertz's minimum age is 18, not 25. There also is an underage driver fee that can be waived with certain CDPs (such as AAA).
The minimum age of 25 only applies for Prestige Collection (Cadillacs/BMWs/Infiniti/etc), Dream Collection (more expensive than previous), and Adrenaline Collection (fast cars such as the Camaro SS or Mustang 5.0).
As long as your daughter is listed on the rental, there should be no issue. Also, if your daughter was prohibited from driving the car (for whatever reason)-- why would it matter if you were sitting in the car with her or not?
Source: am 22, have rented a ton from Hertz