I have just had this work for me. However, it helped my argument quite a bit that I have been "chasing" this bill, have been calling about this bill, have been keeping up with this unsent bill for the last many months.
And yes, I even got the discount for prompt and complete payment, since, as I pointed out to them, this was the first time I had ever received the correct bill in the correct amount for this procedure.
Have you been aware of this bill, did you check with your insurance when you never saw it? Have you spoken to the billing department before? If not, stress this, you haven't heard a word from them. If so, emphasize that you've been making a good faith effort to get this resolved.
Either way, it certainly wouldn't hurt to speak with someone in the office, and request that if you go right on and pay can you get a discount?
But yes, of course you still have to pay it even if it's over a year old.