I'm not sure if you saw my question. Guessing at what you want addressed here is rather difficult, because there are employment law and criminal law aspects to this question. I don't want to address things you are not interested in.
That being said, I'll attempt to formulate an answer without the information I requested.
In employment law, you can legally be terminated without cause unless you have a contract that expressly states you can only be terminated for cause. So, whether they have good evidence or not, they can terminate in this situation if you are without a contract. Even with a contract, if they have some reasonable evidence they can also terminate...even evidence that wouldn't meet criminal law standards (because an employer decision doesn't carry that high of a burden of proof).
In terms of the criminal law aspects here, I'm not sure what you need to know. Yes, they can legally press charges, but the state will decide if there is sufficient evidence to allow for a charge.
If you have any further questions, please let me know. I invite follow up questions, so use REPLY for those. If you have no further questions then good luck going forward and please do not forget to rate my service with a top-three rating so that I receive credit for working with you today. Also, feel free to request me in the future, if you have questions concerning a different matter.