I have a bit different take on this:

"Employers CPA says"

Your taxpayer client doesn't have an Employer, so it will help both of you if you stop referring to it as such. If Employed, that would be a W2. Your taxpayer has a Client who paid for work.

And the work hit $600, for services, so it is reportable as informational. Your taxpayer might have made $3 million, and as long as no one paid $600 or more from their business for your taxpayer's services, you would have no 1099-NEC at all. You still report all of their business income.

"its the clients social and client does not want it revealed, directs me to add the 1099 income directly into C vs into a 1099 tab"

No, you enter all of their business income.

The 1099-NEC informational reporting helps your taxpayer's client prove this is business expense, and reports to the IRS that they can expect a business tax return from your taxpayer.

And yes, people in business should get an EIN and stop using their SSN, as shown by this example.