I can think of a reason to do this:

"Offered money to pay health insurance."

That's just a negotiating concept for setting a compensation package.

"It is paid thru the LLC."

Which might mean the taxpayer got put on a group plan, and that was the attraction. Or, they don't have any plan, so there cannot be pre-tax deduction or employer payment.

"SS and Medi is taxed on the full amount."

I call this "employer is doing the banking." Because really, that's what is happening. The taxpayer's check is reduced and the employer sends on the funds on behalf of the employee to the coverage provider.

And they might have discussed breaking it out like this, because a housekeeper might have independent clients, as well, and files Sched C, and this would provide clarity and documentation for the self-employed health deduction.

As an example.

Many time good intentions don't really stand up to examination. In this case, someone thought it made sense to frame it like this.