"soften the stigma" is the problem here. It's false, dishonest advertisement which means to produce a psychological effect when the practical effect is different. That's why it is called fraud: you say one thing, but sell another, and you know it in advance.
A basic income may or may not be a good policy, but people like Milton Friedman and Charles Murray weren't trying to perpetrate a dishonest fraud (or convince people it's a "free lunch") when they outlined its potential benefits over alternate existing patchwork systems of redistribution.
"Everyone gets it" means to avoid the complexity, corruption, and gaming that comes with an eligibility-testing bureaucracy. "Softens the stigma" means the marginal incentives, especially for the working poor and near poor, aren't muddied by taboos around other welfare programs. (And "softens the stigma" is a honest way to describe that part of the rationale, as well... because some listeners will consider the stigma a good thing, while others see it as a barrier to the policy's intended effects. Universal eligibility does, in actual fact, alter the stigma associated with receiving government income – and people can still argue about whether that's a good thing or not, without allegations of bad-faith fraud.)
