"What is OP"

You are. You are the Original Poster = the person asking.

"and sounds like there is a 50/50 difference of opinion here"

Nope; it's you against everyone else. We all pointed out it has to be part of Payroll, or it doesn't qualify for business and not for QBI, either, because they never "ran it through" the business.

You are overlooking all the activity, here: "If the amount is included in W2 wages, it is offset with deduction on tax return. QBI is unaffected in the end. Obviously the advantage is the S corp picking up the premium tab."

There is no Wash; there is a shifting for reporting.

The Corporation has gross payroll cost, and your client personally has more Taxable income for purposes of Medicare and Social Security. The employer does not have to withhold for Federal Income taxes against the taxable Fringe Benefit, because this person is known to qualify to include this on their 1040 tax return.

Higher Gross Income <== shareholder increase

Higher Gross Expense <== Corporate 1120S

1040 Deduction reduces Gross <== shareholder

the Net = just One deduction happens.

"This, however, is a problem that is unique to S corp as partnerships can get around that by adjusting the distribution instead."

Years ago, S Corp would manage this as Distribution. Then, the IRS started examining what was happening with distribution "abuse" in general. Everything changed. This is the type of thing you would stay current on as part of continuing education and tax regulation updates.

"I am grateful but just wanted a simple answer to my seemingly straightforward question."

Not done with the company = Personal Only. Not QBI, not 1120S, not business. These are the details we learned when you answered our questions and we got better details and more perspective; that always helps you get specific answers.