You can sue anybody you like for just about anything you can think of. Will you prevail? Not likely, unless you can prove falsehood AND actual damages (i.e. - money that you lost because of their false report), not just allege general harm to your credit score. This is very difficult to do and will cost you considerable time and effort.
Demand proof of the debt that you allegedly owe. Clearly one of you is mistaken. Before threatening to sue, see what proof the company has. Then bring that proof to a collection lawyer for assistance.
Yes, anyone can sue anyone for anything, any time, any where for any reason. Will you get summarily dismissed or lose? Sounds like it here. You have to prove actual economic harm and prove to the judge you do not owe the debt and get the judge to find the other party is negligent or willful in wrecking your credit. Showing a dispute and aggressive collection efforts on their part will not be enough.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.