The insurance company is probably not getting ripped off.
When you go to the dentist or doctor, most people do not shop around for price. Therefore, you have no way of knowing what the going market rate is for a particular procedure, and you don't know if you are getting a good deal or not.
Insurance companies, however, know exactly what they should be paying for every procedure, because they deal with lots of providers. That is why they are paying less than the provider billed. Generally, the provider will put whatever they want on the invoice, but the insurance company will only pay up to the current market "fair" price, which they call the negotiated rate.
As long as the invoice that the provider sent accurately names the procedure that you had done, rest assured that the insurance company is paying no more than they want to pay for that procedure.
As to why you got a statement with a smaller amount, it is not uncommon for providers to give a cash discount for people paying without insurance. It saves the provider from insurance paperwork, gets them their payment quicker, and gives a break to patients that don't have insurance.