No, that's not true at all. You should report them to your insurance company, because that's fraud. The insurance company pays them to administer the vaccines - whatever vaccines you choose that are covered at any age, as long as they are covered at that age. For instance, Prevnar might not be covered for a 7-year-old, but it would be covered for an 9-month-old, even though it's recommended you give it at 2,4,6 and 12 (or 18 or whatever that last one is).
It really is fraud for a doctor to try to charge you for that. They sign agreements with the insurance companies on what they can and cannot charge. For instance, almost every insurance company has a rule that they can't except payment from the company and then turn around and charge you on top of that (except for copays and stuff that is specifically described in YOUR insurance policy). If your policy doesn't say you have to pay it, then it's fraud for them to try to charge you that, because they're violating an agreement they made with your insurance company not to scam their clients.
You REALLY need to report that to your insurance company. A doctor who accepts your insurance is not EVER allowed to charge you for anything that's not laid out in your policy, if that's the type of agreement they have. If something isn't covered, your policy will say so and your doctor can then charge you whatever they want for it. Vaccines are covered. They are not covered on any particular schedule. They're just covered. The doctor is trying to circumvent the agreement they made with the insurance companies. Basically, the insurance company says, "We'll reimburse you X amount for Prevnar, X amount for Hib, X for DTaP, etc. That's ALL you can charge for those vaccines, aside from co-pays. You can't collect X from us, then charge our patients Y on top of that." So what the doctor is trying to do, is charge you Y, without saying, "We're charging you Y on top of the amount your insurance pays," since doing so would be a violation of the agreement they have with your insurance company. It's fraud - they're trying to get paid by both you AND the insurance company. They just have to phrase it carefully, so as (hopefully) not to get caught. It's still illegal, so you should report them or threaten to do so. This is why some doctors don't accept insurance at all (reimbursement rates are too low and inability to collect from patients makes it not worthwhile).
At least, it's illegal if they have that sort of agreement with your insurance company, which they probably do as it's relatively standard. Read your policy. Most of them will specifically say that a doctor can't charge you more than what they've agreed to accept from the insurance company. If there are exceptions to that rule (there sometimes are) then that will also be explained in the policy. Please don't just pay it without verifying that your insurance company allows this. Your insurance company probably does not allow this.