Arresting a suspect with PC?

In many cases PC is established and an arrest is sought. What happens if you arrest the suspect and he has a complete innocent reason to dispute the evidence against them. For instance, you have a burglary to a vehicle. Evidence techs process the vehicle and find prints INSIDE the car. The prints match a person in the system. This is enough to arrest. What if after the arrest the person admits to being there, but not committing the crime. They may come up with an innocent reason like that they locked the car back up trying to help, and they did not want to wait for the police. Although odd, it is completely conceivable. Or what if there is a murder or robbery, the victims neighbor that has never been to the house before enters, because he has noticed something is not right. Upon entering he finds the dead body, and freaks out and leaves, and decides not to call the police out of fear. Their prints may be found at the scene, and be enough for PC. But this person obviously did not commit the crime. In these rare but innocent situation that do happen, would an arrest still be justified, or should these individuals be questioned first?