Tippit was certainly a hero and played a significant role in bringing Oswald to justice. Who knows how long Oswald might have been on the run had Tippit not stopped to question? We can never know all the details of that interaction but Oswald most likely saw Tippit's police car and made some movement that aroused Tippit's suspicion. Tippit pulls over to check it out. Oswald tries to bluff his way out but can't ID himself because he may already be a suspect in the assassination. So he is evasive. Tippit decides to get out of the car and investigate further. Oswald decides to act while he still has the element of surprise. You do have to feel bad for the Tippit family. They not only lost a husband and father but have also been subject to insane conspiracy theories for decades.
