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A common assumption about the NST is that it is naturally regressive, since lower income individuals spend a greater percentage of their income in any given year on consumption of necessities. Because a sales tax is an altogether different paradigm of taxation, any judgment on the equity of the tax must be accompanied by a different analysis of regressivity.
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It's nice to say it requires a different analysis of regressivity because it is a different paradigm, but that doesn't really mean a whole lot.
In the example I gave above, Person A/Person B, the 7% and 3% tax rates are not real tax rates, the real tax rate is 20%. The 7 and 3 are comparative tax rates to the income-based tax system. In essence, we look at how much consumptive tax is paid by each person and view that as a percentage of the income. It certainly is an analysis along the lines of our current system applied to an entirely different system. But at the same time, the result of the analysis is applicable as a comparison to our current system.
As your source stated, consumption spending does not increase equivalent to an increase in income, which I have mentioned a few times now. It offers a remedy of adding in an essentially arbitrary number (poverty level) to bring back some of the progressivity it had eliminated. The effect is nothing more than an artificial crutch for the failings in the consumption-based tax plan. Maybe there's a term for it, but if you think of a curve on a graph, the arbitrary number simply levels out, flattens, the first segment, then the curve continues on it's way, unadjusted. (The curve being the regressivity of the tax system.)
Maybe smooth's suggestion of localized cost of living would be more applicable than poverty level - but it would still be an artificial crutch for the system.
Speaking of this arbitrary number - where did they come up with the poverty level as the number that would be appropriate? If the system is based on consumption, why is the "fix" to the flaw in the system a number based on income?