Can security guards lie about having footage of you doing something illegal?

I was in Wal-Mart with my friends one time, and we all went into the bathroom to **** around, ****, etc. My friend found an empty CD case in one of the stalls so we decided to give it to a clerk. We thought it would be a good gesture to let them know that someone had stolen from them. Maybe it would help them keep inventory. Well, fifteen minutes and a purchased CD later we decided to leave; except we couldn't! As we tried to leave, two security guards walked up to us and started accusing us of stealing a CD. This, of course, is understandable seeing as though we had handed them the earlier CD case. Maybe they thought we were covering it up or something. My anger was also reasonable, because I hadn't stolen jack ****. But, later into the conversation, one of the security guards started telling me that they actually had footage of us stealing the CD. I immediately called their bluff and told them to show me this god damn footage. After he yzed us and decided we hadn't stolen anything, the security guard let us go. Leaving Wal-Mart pissed off, I wondered if they're even allowed to lie about those things. In an earlier situation, a policeman was interrogating me some car hopping that had been happening in my neighborhood. He also hinted that he had footage of me by saying, "Sometimes the park district sets up random security cameras," and hinting at other stupid things. Seeing as though a full-fledged officer of the law never actually lied about having footage of me and only hinted, I was wondering if security guards, or even police officers, are allowed to lie about these things. I ume they are, but I'd like to know.