Pymnt in full and up front w/a discount is usually reserved for self-pay pt's as Tessa stated. The discount a patient receives if they have insurance is the contracted rate and pymnt reduction a provider has with a payor.
Hence many practices do not offer a chance for a discount after the payor has paid, even if the patient is going to pay the balance in full. "You already received a discount when your 'insurance' processed and reimbursed our practice."
As Cyndee said, if you give an insured patient a discount upfront for paying in full, then send the claim to the insurance for reimbursement w/o the discount, you are committing fraud. Practices have contracts w/insurances. Patients have contracts w/insurances including deductibles and co-insurance. You cannot forgive the patient their deductible or co-insurance or parts thereof unless the insurance did. Copays on the other hand can be forgiven (to my knowledge, but it's an across the board thing and has to be offered to everyone and also another argument for another time) but best not since that's "freeflowing" money collected up front and can be a lifeline of cash.
Look at it like this, Medicare only allows so much, you can't bill the patient the leftover, that's balance billing. Same thing here in reverse, You allow the patient only so much but then bill the insurance, balance billing, and it's against most contracts.