The standard advice I have seen about how to deal with a confrontation by an LP is to demand that they state why they are detaining you, remain in a public place, and call 911 to report unlawful detention. Once the store management realizes that a mistake has been made, demand a public apology and the termination of the employee involved or you will be filing suit. They will trip over themselves to comply. And just to make sure that we are on the same page, if I detain you because I have a reasonable belief that you are leaving my store without paying for my merchandise, then you are in no position to make demands, If you feel that your have been unreasonably detained, then I'll see you in court.
Wrong: I can demand you state why you are detaining me. (which is exactly what I stated earlier). Failure to clearly state the reason and thereby invoke Storekeeper's Privilege (it does not have to be explicit) means you are breaking the law.
If I have not been in your store (as in the case I cited earlier) I am free to ignore you and leave the parking lot Any actions you take to prevent that are unlawful at that point. Mistaken identity is not an affirmative defense for A&B and unlawful detention.
The key item is what is reasonable suspicion. If you are wrong the person you accused can do devastating things to your life in addition to your employer dumping you like week old fish. Seen it happen more than once.