i worked for a hospital that never got around to verifying licenses. i decided to see how long it would take before they checked mine, since i got the mandatory reminder from the nursing office to bring it in. i went to the hospital risk manager and showed it to her, and told her what i was up to. she was surprised but gave me six weeks. at the end of that, she went and asked the nursing office about my licence, and when they couldn't tell her i was current she had her answer. they got better about it after that, and i got one more reason for people to call me a trouble-maker.
of course it's illegal to call yourself rn or allow someone else to believe you are if you are not. it is not "no big deal." that said, either report her to the bon or stop with the sleuthing and drama. decide what's important to you, then do it.