The right way to look at this....
The right way to look at tax burdens is not share of each income group in total tax receipts, but share of each groups' income going to taxes.
Simple illustration. We have a population of 10, 9 of whom are poor and 1 rich.
Year 1:
9 poor: Income = 1000, Taxes each = 100
1 rich: Income = 10000, Taxes = 1000
Tax revenue share: 47% from poor, 53% from rich
Tax burden: 10% on each
Year 2:
9 poor: Income = 500, Taxes each = 90
1 rich: Income = 50000, Taxes = 1090
Revenue share: 42% from poor, 58% from rich
Tax burden: 18% on poor, 2% on rich
By your logic, TB, Year 1 is more fair to the rich guy, and the poor ought to be happy in Year 2.