If a Doctor incorporated, does another company that hired his as a contractor still needs to issue 1099 MISC to that doctor.

Who was hired?

Dr. John Smith

or John Smith MD, PC?

Many of us have seen corporations where the owners do not follow the formalities.

And it would be 1099-NEC.

Seems clear to me.  Are you a tax practitioner, or a medical practitioner fishing for an answer that conforms to what you think the law should be, rather than what it is?

Box 6. Medical and Health Care Payments
Enter payments of $600 or more made in the course of your
trade or business to each physician or other supplier or
provider of medical or health care services. Include payments
made by medical and health care insurers under health,
accident, and sickness insurance programs. If payment is
made to a corporation, list the corporation as the recipient
rather than the individual providing the services. Payments to
persons providing health care services often include charges
for injections, drugs, dentures, and similar items. In these
cases, the entire payment is subject to information reporting.
You are not required to report payments to pharmacies for
prescription drugs.
The exemption from issuing Form 1099-MISC to a
corporation does not apply to payments for medical or health
care services provided by corporations, including
professional corporations.

"That incorporated doctor provides medical service to a patient, not to a company that pays him."

The patient isn't trying to include that cost in their business activity. The company paying the doctor has the business relationship, and that is why they fall under the 1099 reporting rules. Even buying into your perspective, the 1099-Misc instructions include reporting payments you are making on behalf of another party, such as a law firm has a lawsuit which involves hiring a medical professional to do a patient assessment for purposes of negotiating a settlement amount. If you ever work with an employer who falls under DOT rules, they hire doctors and phlebotomists all the time, and they do lots of this reporting.

"Therefore the incorporated doctor does not need 1099 MISC. Am I correct here?"

Corporation reporting for medical is one of the many exceptions which require reporting. From the IRS 1099-Misc and -NEC: https://www.irs.gov/pub/irs-pdf/i1099mec.pdf