I received this email from Barbara,
Well, it's a little hard for me to give a precise opinion without knowing more details about the case, such as exactly what is meant by "extensive dental work". However, I can imagine that there may be receeded gums, periodontal disease, loose teeth, and so on. If such is the case, then simply cleaning the teeth isn't going to help.
Let's say that you have a car that isn't in the best of shape. The floorboards are rusting, the tires are balding, and the bumper is hanging at an odd angle. So you decide to spend a hundred dollars to get it professionally waxed and detailed. Does it look better? Sure! Have you don't anything to fix the car? Nope. You may still have a bumper fall off, tires that aren't safe, and might put your foot through the bottom of the car. So what have you really done to help your car be safer? Nothing. What was the purpose of spending the money merely to make it look better?
While not a perfect analogy, you can use it to describe teeth. When there is periodontal disease, especially with loose teeth or erosion of bone, doing a basic dental cleaning isn't going to help. That's like washing and waxing a rusting car. In order to fix the problem you have to get below the gumline, extract infected teeth, and treat the problem. If you merely clean the tartar away and polish the teeth you haven't actually fixed anything. In fact, you've ignored the real problem that is brewing where you can't easily see it. Since you're putting the patient under anesthesia with those associated risks, you are doing a procedure that doesn't really fix anything. Sure, the teeth look a little better but that's a false sense of security. The problem is still there and you've spent the money without truly fixing anything.
In similar situations I have also refused a basic dental cleaning. I don't know if that's the case with your dog, Barbara, but I hope this explains it a little better.