Beware the logical fallacy. "A implies B" does not mean that "not A implies not B".

Workers who earn too little to pay taxes (A) will not benefit from a tax cut (B).

But workers who earn enough (not A) may still not benefit (not B), for example because their employer indirectly pockets the difference. That is actually being argued in the article.

So this is indeed the appropriate way of formulating the statement: at least 40% of workers will demonstrably not benefit from this.

Well, to be fair, the IRS considers the average tip to be 8% for taxation purposes.

The whole "I get taxed whether you tip me or not", "I have to pay to serve you if you don't tip"? No, not so much. If you can show (there's even a hugely burdensome IRS form that might take as much as 3-4 minutes a month for cash tips) that you earned less than that 8% average, then that's what you get taxed. But most servers don't want to fill that form out, because they get ... rather more than that, and are being undertaxed already.

it's indirect tax credits for businesses that don't want to pay workers.

The tax system is graduated. If 40% don’t make enough to hit a band where income is taxed, then you can assume it’s a gentle ride from paying no taxes to not paying much taxes. And anyways, payroll taxes are by far the higher burden for service workers than income taxes.

Sure, but TFA makes clear that any benefit to workers from tax-free tips is laughable compared to the numbers of times the restaurant lobby has fucked them over, by repeatedly killing attempts to keep wages low. It's not even throwing workers scraps, it's more like throwing them crumbs.