One of the most boisterous, buffoonish characters in the Dragon Ball franchise is Hercule Satan, introduced at the start of the Cell Games Saga in Dragon Ball Z. Taking credit for Gohan destroying Cell, Hercule was immediately revered as the strongest man in the world and the savior of humanity for dispatching the villain.
Seven years later, Hercule's teenage daughter Videl sought to follow in her father's footsteps by fighting crime in the streets of Satan City while balancing her academic responsibilities in high school. However, with Hercule being such a massive fraud, the real question is why he allowed his only child to constantly put herself in harm's way.
When Gohan meets Videl, she is already an established crimefighter, working directly alongside the Satan City Police Department in busting criminals and providing support during other emergency situations. By the end of DBZ, Videl decided to become a full-on superhero, fighting alongside Gohan in her own costumed persona as Saiyagirl or the Great Saiyaman II.
And through it all, Hercule never steps in to intervene or dissuade Videl from fighting against legitimate threats. This complacency is tied to Videl's upbringing and her natural tenacity as she tries to prove herself worthy enough of being Hercule's daughter, secretly far surpassing her father through a lifetime of training and special instruction from Gohan.
It is revealed that at the age of 11, approximately the same age that Gohan destroyed Cell, Videl owned the Junior Division of the 24th World Martial Arts Tournament, already making her one of the world's greatest fighters. Videl and Hercule's home also boasts a state-of-the-art athletic facility and training staff, with both seen separately yet diligently training in martial arts. This established competency -- and Hercule's awareness that Videl is working alongside the police -- that likely makes him comfortable and confident enough in permitting her to have an active crimefighting career. This is further evidenced with Hercule's surprise when he learns that Videl was beaten by Spopovich in the adult World Martial Arts Tournament.
The other factor is that Videl has never really been a character to take no for an answer. When Gohan initially declined to teach her how to fly, she essentially blackmailed him into complying over the knowledge of his superhero secret identity. Videl would also insist on accompanying Gohan to confront the evil wizard Babidi before quickly realizing she was outmatched and deciding to let him proceed without her.
While many of Videl's cinematic appearances are non-canonical, they still demonstrate a woman unafraid to face more powerful opponents, even taking on Broly in the 1994 anime film Dragon Ball: Broly - Second Coming and an army of undead villains in 1995's Dragon Ball Z: Fusion Reborn.
Videl is one of the bravest Z Fighters and quietly one of the strongest humans in the world, able to stand toe-to-toe against magically enhanced opponents and fly at an age where many of the Z Fighters struggled to achieve the ability. Hercule is unaware of the full extent of Videl's potential but knows she is a formidable fighter in her own right. Even before meeting Gohan and having her life changed forever, Videl was out there fighting crime with her father's apparent blessing while being stronger than him all along -- and Hercule was none the wiser of his daughter's abilities.