Absolutely it does get around the cost issue. Someone with no income receives just a UBI. They cost the system $20. Someone with non-zero income recives both a UBI and a higher income tax burden. What net impact does that individual have on the cost of the system? If their income is greater than the UBI... the impact might be zero, or negative.

Assuming a 40% tax (no idea what it would actually be in practice), everyone earning less than $50 a month would be a net cost.

As a thought experiment, imagine that you increased the UBI payments so that they took up all the gross income of the country. Now your tax rates are 100%, even though the "net impact" of the redistribution is 0. A smaller UBI is the same concept, just the percent of income distributed is smaller. The bigger the UBI, the larger your tax rates on all workers. As those tax rates reduce the supply of labour, the costs mount even more.