Indeed. For example, the parent's suggested scheme is equivalent to a $15k basic income, with a 25% tax on earned income up to $60k.

The only real difference between the two is the constants each framing leads us towards. The above scheme is fairly mild, but if you shrink the window down to $30k, which initially sounds progressive (less money for richer people right?) you actually end up with the equivalent of a 50% tax band on income below $30k.

I prefer the Basic Income framing for this reason.

Yes, you figured out why I picked the numbers I did. It's somewhat surprising how high the full phase-out amount has to be for things to work: It basically needs to go to several times the poverty level in order to make the marginal taxation on poor people of acceptably low levels.