Did your wife give notice at all? Or was she planning to leave that same day? It might hinge on the substance of the long talk. If she started out the talk with her manager by giving her 2 weeks' notice, and after the long talk, they agreed that night would be her last, to me that might be characterized as an involuntary term, rather than a resignation - even if she started out the conversation by giving her resignation.
They are insisting she was fired. If she did want to walk away that same day, they may be claiming she was fired to send a message to the remaining staff. They may be very angry about her giving up her job, because it sounds like it would be a difficult one to fill.
DOL does not care about her being fired or if she resigned, unless she files a claim for UI benefits. If she does that, they have a copy of her written resignation, but the letter they mailed to her saying that she was fired does give her a lot of mileage on her own claim. I would tread carefully with that if she decides to do it, because they may say one thing to her and to staff, but a different story to the state.
Michigan's nursing board has procedures to follow for filing complaints about licensed professionals, including nurses.
Here's a link for her to check on her license:
http://www7.dleg.state.mi.us/free/
Here's a link to how the allegation/investigation procedure works:
http://www.michigan.gov/lara/0,1607,...3590--,00.html
Hope that helps.