Lots of companies do this, they normally just pass those files over to a debt collector and/or a lawyer and these people will get commission for any debt collected. That's why they are so persistent.
My company has similar case with Telekom Malaysia, they claim that I owe them this amount of money which I have never renew that particular plan and also they acknowledge my letter of cancellation. Worst thing is, this was cancelled way back in 2002 and recently they came and kacau again. They will always send a different lawyer or debt collector firm to threaten you, with lots of notice letters, warnings and phone calls made to all the staff of the company. They won't really sue you, they just threaten only. Lots of people shiver when they receive lawyer warning letter or hear that big companies wanna sue them.

Go directly to courts and demand for a clarification. Show all your receipts and keep every single letter. Write back to them in black and white with the prove and everything also. Chances are they will keep quiet for now, promise to update their accounts, pass you here and there from one person to another, andden after few years will come back and haunt you again if they lazy to update their accounts.
Don't think you can do much with a court case, lawyer fees not cheap these days. Your bosses should understand that this sort of things happen and you can always explain to them that it's the courts company that never update the accounts. If they really wanna make a big fuss about it, show them the receipts then. Embarrassment don't think can sue much, unless it's like you lost your job/business because of it. Anyway, try consulting a lawyer and see how it goes.