Yeah, I feel like you misunderstand how a negative income tax works. There would be absolutely zero invasion of privacy, because there is no longer a requirement for eligibility. As with a UBI, everyone would get a payment (although for most people it would simply be a credit towards their income tax bill).
The main advantages of a negative income tax are:
- A flat income tax rate (I won't go into the many benefits of a flat income tax rate, but there are a lot)
- Elimination of "welfare cliffs"—where benefits are cut off once someone starts earning, discouraging work
- Reduction of government administrative costs by eliminating eligibility tests
- no retirement age - the UBI would simply continue into old age. You can choose to top it up with additional work or investment income
It's surprising how close the implementation of this mirrors the actual current situation in Australia (see chart below in AUD with an annual UBI of $19,830 - equivalent to the current social security payment - and a flat tax rate of 47% - equivalent to the current top rate of income tax). Unsure how it would look in other countries, but I suspect the figures can be tweaked to align.