Is that her SSN or the S Corp EIN on the 1099?

If she was doing the same work at the dental office for her S Corp as she did for others, then she should be contracting as acting on behalf of the S Corp. She submits a W9, as well, to these customers (which is not the patients, but these other dental offices or hospitals) so that it is clear they are contracting for her services through her professional entity.

"and she was an Independent Contractor Dentist for several other dental offices."

This is often an issue with perspective.Yes, no matter which way this gets contracted, since she is not being hired as an employee of the other dental offices, she is independent. As a person working for her own entity, she (via her corporation) can contract with others. That means these other dental offices would be her Clients, under contract. The contract between herself, as President of the Corporation and the licensed dentist, is independent to those clinics. They are not hiring her, as an employee. They are contracting for her services, which should have been done under the S Corp.

There are some circumstances where a person has a business entity as the S Corp, and performs other services not under the S Corp. Example: A S Corp for the dental practice and an LLP for a traveling mobile clinic partnered with other dentists. There are reasons to separate functions into separate entities, for liability purposes, for instance.

"Independent contractor" does not also mean "Not Corporation." It means, "Not our employee" for her customers with whom she contracts to provide her services.

I'm surprised there isn't some State licensing or insurance requirement that she isn't supposed to be working under her SSN.

It's not too late to fix this for 2023.

"I assume Shareholder Distribution, however, that would create a Capital Gain distribution to the Shareholder(She is the sole shareholder)."

Nope. She is supposed to get paid reasonable wages for services, through payroll. A distribution from an S Corp isn't a Capital Gain distribution. There are different types of Distributions.

How did she handle payroll? Did she keep all the funds from those "independent" jobs herself, directly, or run them through the S Corp as payroll?