Perhaps that was the wrong wording, but giving everyone money would only inflate costs as they rise to meet the new income levels (whether that money is printed or redistributed). What else are you claiming is made up?
"Motivates working, avoids a blanket handout which would just raise the prices of everything in response"
"More fair, less cost, and better purchasing power"
I mean that it's a made up difference between UBI and NIT, they are simply equal in this regard, for better or for worse.
It makes no sense that they would be different, as the net money flow between individual (or household) and the government can be made exactly the same between UBI and NIT scheme, and how much money someone actually has in their hands is what determines motivation, fairness, purchasing power, inflation etc.
Under UBI: NetMonthlyIncome = income + UBI - taxes_ubi(income)
Under NIT (where taxes_nit can yield a negative value): NetMonthlyIncome = income - taxes_nit(income)
You can make taxes_ubi(income) == taxes_nit(income) + UBI and you get the same exact real life result, it's just that the accounting is different.
UBI and NIT are two different systems that provide the same minimum income guarantee. Saying they both provide a min income is obvious. That's what they're designed to do.
However the way they do it is very different and that's what changes everything. NIT guarantees min. income without just paying everyone. This costs less than UBI. NIT pays a (negative tax) bonus on the first dollars instead of immediately taxing earnings. This provides more motivation. Not giving everyone the same helicopter money prevents cost of living inflation. This provides better purchasing power.
How you provide the income is more important the final amount because the economy is an interconnected system with secondary effects. This is why Friedman recommended NIT instead of UBI. The mechanics of the system matter.