An example that proves you wrong.
You hear a yell and turn your head. You see a woman yelling, “he stole my purse” and points at a man running with a pink purse in his hand.
You didn’t see him take the purse. You however, have probable reason to believe a crime occurred.
In your scenario, it would be wrong for a CIVILIAN to use force to restrain a person whom they did not see commit a crime. Why don't you people understand the differences between what civilians can do and what cops can do???
In your scenario, the person could absolutely pursue the suspect and tell the 911 operator the location of the suspect until police arrive. But any decent defense lawyer would have a field day if a civilian did not actually see the crime and used force to restrain a suspect.