Can police ticket you for something they never caught you doing?

I was given a ticket for being in the park after hours. The cop put me into the backseat of his car and had my phone with him. One of my friends I was with, but who didnt get semi arrested by the cops, called my phone. The cop then preceded to call him back twice, and then went through my phone. He asked me the names of the people I was with, and he double checked them on my phone. He then let me go with a ticket. I went to court and plead guilty and now have to pay a fine. My friends on the other hand got tickets for the same offense in the mail. However, the cop never once talked to any of them. The cop also called my friend and told him that I told on all of them. I never gave the cop any of their address or phone numbers, yet he had all of them. To add to this, the cop never read me my rights if that changes anything. I already am paying the fine, but what should my friends do being that they never talked to the cop and yet are facing a fine?