In the states I believe the process you're describing is called "means testing." It's how the government determines whether someone can receive food stamps or other government assistance: checking first if they really need it, do they have the means to buy food, etc.

The advantage of UBI is that the question of who has a right to claim the benefit is completely sidestepped, and so is the accompanying bureaucracy and barriers.

You're right, rich people don't need UBI. At the same time - much harder to complain about something everyone gets. Much harder to take back a right that all citizens have, than "charity" that only the powerless receive. Harder to call people "welfare queens".